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Wikipedia:WikiProject Mathematics/PlanetMath Exchange/20-XX Group theory and generalizations

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This page provides a list of all articles available at PlanetMath in the following topic:

20-XX Group theory and generalizations.

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A adequately covered
C copied
M merged
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20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

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Jtwdog 16:55, 20 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
AdamSmithee 09:01, 12 January 2006 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
Jtwdog 18:08, 19 October 2005 (UTC)[reply]
AdamSmithee 08:47, 7 March 2006 (UTC)[reply]

20-01 Instructional exposition (textbooks, tutorial papers, etc.)

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20-02 Research exposition (monographs, survey articles)

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Jtwdog 21:15, 28 October 2005 (UTC)[reply]

20A05 Axiomatics and elementary properties

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Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 18:17, 19 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)[reply]
I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
Jtwdog 17:26, 20 October 2005 (UTC)[reply]
linas 23:45, 6 April 2007 (UTC)[reply]
I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)[reply]

20A99 Miscellaneous

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Jtwdog 17:50, 26 October 2005 (UTC)[reply]
Some work needs to be done here to draw the distinctions between direct sum and direct product. Merging together the two articles might be a good idea. Jtwdog 17:50, 26 October 2005 (UTC)[reply]
Jtwdog 17:50, 26 October 2005 (UTC)[reply]
Jtwdog 17:50, 26 October 2005 (UTC)[reply]

20Axx Foundations

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20B05 General theory for finite groups

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Jtwdog 21:31, 26 September 2005 (UTC)[reply]

20B15 Primitive groups

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Jtwdog 21:31, 26 September 2005 (UTC)[reply]

20B20 Multiply transitive finite groups

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Jtwdog 19:48, 26 October 2005 (UTC)[reply]
Jtwdog 19:48, 26 October 2005 (UTC)[reply]
Jtwdog 19:48, 26 October 2005 (UTC)[reply]

20B30 Symmetric groups

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Jtwdog 18:21, 19 October 2005 (UTC)[reply]
Jtwdog 18:21, 19 October 2005 (UTC)[reply]

20B35 Subgroups of symmetric groups

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Jtwdog 18:21, 19 October 2005 (UTC)[reply]

20B40 Computational methods

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20B99 Miscellaneous

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Jtwdog 18:22, 19 October 2005 (UTC)[reply]
Jtwdog 18:22, 19 October 2005 (UTC)[reply]

20Bxx Permutation groups

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20C05 Group rings of finite groups and their modules

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20C07 Group rings of infinite groups and their modules

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20C08 Hecke algebras and their representations

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20C15 Ordinary representations and characters

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It's nice to include counter-examples, though this is probably a low priority. Jtwdog 20:26, 26 October 2005 (UTC)[reply]
Jtwdog 20:26, 26 October 2005 (UTC)[reply]
It would be nice to bring over a little of the proof, as I think it's quite beautiful, but I'll leave that to other's judgement.Jtwdog 20:26, 26 October 2005 (UTC)[reply]
Jtwdog 20:26, 26 October 2005 (UTC)[reply]

20C30 Representations of finite symmetric groups

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20C35 Applications of group representations to physics

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20C99 Miscellaneous

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Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]
Jtwdog 04:08, 28 October 2005 (UTC)[reply]

20Cxx Representation theory of groups

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20D05 Classification of simple and nonsolvable groups

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Oleg Alexandrov (talk) 23:05, 21 November 2005 (UTC)[reply]

20D06 Simple groups: alternating groups and groups of Lie type

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Jtwdog 04:09, 28 October 2005 (UTC)[reply]
Its a proof; added ref to simple group. linas 23:03, 6 April 2007 (UTC)[reply]

20D08 Simple groups: sporadic groups

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Jtwdog 04:10, 28 October 2005 (UTC)[reply]

20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks

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20D15 Nilpotent groups, $p$-groups

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20D20 Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

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20D25 Special subgroups (Frattini, Fitting, etc.)

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20D30 Series and lattices of subgroups

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20D35 Subnormal subgroups

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Jtwdog 23:49, 2 October 2005 (UTC)[reply]

20D60 Arithmetic and combinatorial problems

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20D99 Miscellaneous

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The ling is currently redirecting to Order (group theory), which mentions the theorem in passing (anyway, the article should be cleaned up). I think that something more like Lagrange's theorem (group theory) would be more appropriate AdamSmithee 09:28, 12 January 2006 (UTC)[reply]
Done AdamSmithee 09:26, 7 March 2006 (UTC)[reply]
Oleg Alexandrov (talk) 04:15, 22 January 2007 (UTC)[reply]
AdamSmithee 09:28, 12 January 2006 (UTC)[reply]
NM after creation of the WP article - see above AdamSmithee 09:28, 12 January 2006 (UTC)[reply]
Actually, on a second thought, this is not a particularly illuminating proof. I linked to it AdamSmithee 09:26, 7 March 2006 (UTC)[reply]
AdamSmithee 09:28, 12 January 2006 (UTC)[reply]

20Dxx Abstract finite groups

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20E05 Free nonabelian groups

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20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

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linas 22:08, 6 April 2007 (UTC)[reply]
linas 22:30, 6 April 2007 (UTC)[reply]

20E07 Subgroup theorems; subgroup growth

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20E10 Quasivarieties and varieties of groups

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20E15 Chains and lattices of subgroups, subnormal subgroups

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20E18 Limits, profinite groups

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Jtwdog 23:47, 2 October 2005 (UTC)[reply]

20E22 Extensions, wreath products, and other compositions

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20E25 Local properties

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Oleg Alexandrov (talk) 04:17, 22 January 2007 (UTC)[reply]

20E26 Residual properties and generalizations

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20E28 Maximal subgroups

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20E32 Simple groups

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20E34 General structure theorems

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20E36 General theorems concerning automorphisms of groups

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20E45 Conjugacy classes

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Jtwdog 23:44, 2 October 2005 (UTC)[reply]

20E99 Miscellaneous

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Jtwdog 23:46, 2 October 2005 (UTC)[reply]
Jtwdog 23:46, 2 October 2005 (UTC)[reply]

20Exx Structure and classification of infinite or finite groups

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20F05 Generators, relations, and presentations

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20F06 Cancellation theory; application of van Kampen diagrams

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20F10 Word problems, other decision problems, connections with logic and automata

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20F12 Commutator calculus

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20F14 Derived series, central series, and generalizations

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20F16 Solvable groups, supersolvable groups

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20F18 Nilpotent groups

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Jtwdog 23:38, 2 October 2005 (UTC)[reply]

20F19 Generalizations of solvable and nilpotent groups

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20F22 Other classes of groups defined by subgroup chains

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Jtwdog 23:40, 2 October 2005 (UTC)[reply]

20F24 FC-groups and their generalizations

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20F28 Automorphism groups of groups

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20F34 Fundamental groups and their automorphisms

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20F36 Braid groups; Artin groups

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Jtwdog 04:12, 28 October 2005 (UTC)[reply]
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20F50 Periodic groups; locally finite groups

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20F55 Reflection and Coxeter groups

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Jtwdog 04:14, 28 October 2005 (UTC)[reply]
Jtwdog 04:14, 28 October 2005 (UTC)[reply]

20F60 Ordered groups

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20F65 Geometric group theory

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20F69 Asymptotic properties of groups

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20F99 Miscellaneous

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Jtwdog 04:14, 28 October 2005 (UTC)[reply]

20Fxx Special aspects of infinite or finite groups

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20G15 Linear algebraic groups over arbitrary fields

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20G20 Linear algebraic groups over the reals, the complexes, the quaternions

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AdamSmithee 09:42, 7 March 2006 (UTC)[reply]

20G25 Linear algebraic groups over local fields and their integers

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20G40 Linear algebraic groups over finite fields

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20Gxx Linear algebraic groups (classical groups)

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20H05 Unimodular groups, congruence subgroups

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20H20 Other matrix groups over fields

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20Hxx Other groups of matrices

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20J05 Homological methods in group theory

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20J06 Cohomology of groups

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Jtwdog 19:33, 1 November 2005 (UTC)[reply]
Jtwdog 19:33, 1 November 2005 (UTC)[reply]
Jtwdog 19:33, 1 November 2005 (UTC)[reply]

20J15 Category of groups

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20Jxx Connections with homological algebra and category theory

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20K01 Finite abelian groups

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20K10 Torsion groups, primary groups and generalized primary groups

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Jtwdog 23:37, 2 October 2005 (UTC)[reply]

20K15 Torsion-free groups, finite rank

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20K20 Torsion-free groups, infinite rank

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20K25 Direct sums, direct products, etc.

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20K27 Subgroups

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20K30 Automorphisms, homomorphisms, endomorphisms, etc.

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20K35 Extensions

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20K99 Miscellaneous

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Jtwdog 21:33, 26 September 2005 (UTC)[reply]
Jtwdog 21:33, 26 September 2005 (UTC)[reply]
Jtwdog 21:33, 26 September 2005 (UTC)[reply]

20Kxx Abelian groups

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20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)

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20M05 Free semigroups, generators and relations, word problems

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20M10 General structure theory

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20M12 Ideal theory

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20M14 Commutative semigroups

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20M17 Regular semigroups

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20M18 Inverse semigroups

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20M20 Semigroups of transformations, etc.

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20M30 Representation of semigroups; actions of semigroups on sets

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Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]
Jtwdog 23:35, 2 October 2005 (UTC)[reply]

20M35 Semigroups in automata theory, linguistics, etc.

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Jtwdog 23:27, 2 October 2005 (UTC)[reply]
Jtwdog 23:27, 2 October 2005 (UTC)[reply]
Jtwdog 23:27, 2 October 2005 (UTC)[reply]

20M99 Miscellaneous

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  • PM: band, id=3319 -- WP guess: band -- Status:
AdamSmithee 09:35, 12 January 2006 (UTC)[reply]
  • PM: rig, id=6378 -- WP guess: rig -- Status:
AdamSmithee 09:35, 12 January 2006 (UTC)[reply]
AdamSmithee 09:35, 12 January 2006 (UTC)[reply]

20Mxx Semigroups

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20N02 Sets with a single binary operation (groupoids)

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Jtwdog 23:24, 2 October 2005 (UTC)[reply]
Jtwdog 23:24, 2 October 2005 (UTC)[reply]

20N05 Loops, quasigroups

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Oleg Alexandrov (talk) 04:18, 22 January 2007 (UTC)[reply]

20Nxx Other generalizations of groups

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