Talk:Glossary of group theory
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It says, "Order of an element of a group. Suppose x∈G and there exists a positive integer m such that xm = e, then the smallest possible m is called the order of x. The order of a finite group is divisible by the order of every element."
What is e? Is e∈G true? dave 21:07, 8 Sep 2004 (UTC)
e is the identity element of the group. So yes, e∈G is true.
Glossary Symbology
editI am working on a Sudoku maths page, and will be working through (as in referencing, using) the Group theory articles. I would like to incorporate the symbololgy (denoting symbols) from the other articles in the/this glossary. If no one objects, I will do so. Principally I don't like duplicating info, which creates an update sync. headache, but here I think it's appropriate. --LarryLACa 17:02, 9 October 2005 (UTC)
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Notation
editWould it be appropriate for this page to explain the notation it uses, or at least link each first instance of a notation to page where that notation is explained? I am thinking in particular of the notation of S within pointy parentheses, with which I am not familiar, and which I don't know how to type here without adding strikethroughs. I am sure I could find it, but I think it would make sense for the page to do that work for the reader (in terms of explaining the notation, not the strikethroughs, obviously). 69.205.34.127 (talk) 03:30, 2 February 2008 (UTC)pj.deBarros@gmail.com
Question on notation
editIs there somewhere that the notation used here:
- A group (G, •)
is described in more detail? I think it might relate to the page Structure (mathematical logic), but I'm not sure.
In particular, I'd like to know what such notation is intended to capture about the object of interest. It seems odd for it to capture only part of the story, with extra concerns tacked on ad hoc, such as requirements for associativity, inverse and so on.
This seems to be behind the later comment:
- In universal algebra, groups are generally treated as algebraic structures of the form (G, •, e, −1),
(though the referenced universal algebra page doesn't mention this notation). At any rate, this notation captures more of the features of the object, but still not all. Very haphazard seeming.
So I'd like to understand more about what conventions this notation is based on, and that info might be useful to present in this article. Gwideman (talk) 20:18, 10 December 2009 (UTC)
Semigroups and symmetric groups not defined
editThe term semigroup isn't defined but it is used in the article. What is the point of an article defining some basic terms in group theory if it relies on a prior understanding of terms like semigroup. This defeats the purpose of the article!
Note that this article is now linked to under "basic notions" in the group theory side bar that is on group theory articles. Yet this article will remain anything but "basic" if terms like the above send the reader on an endless link chase through articles that presuppose the basic understanding that they sought in the first place. Ross Fraser (talk) 00:16, 30 October 2010 (UTC)
How is this a glossary?
editI don't see how the page glossary of group theory can be called a glossary. It doesn't conform to the definition at glossary, nor to the one at Wikipedia:Manual of Style/Glossaries. In its current form it is largely redundant with group (mathematics). — Tobias Bergemann (talk) 10:15, 18 October 2012 (UTC)
Restored after discussion
editGlossary of group theory had been moved to Group theory terminology in 2015, and that article was then AfD'd (Wikipedia:Articles for deletion/Group theory terminology) and turned into a redirect to Group theory. After discussion at Wikipedia:Redirects for discussion/Log/2020 June 17#Glossary of group theory, the article has now been restored/moved back to Glossary of group theory, and I now have restored the last revision (from 2008) that actually looked like some glossary. However, more work is necessary. If you can, please help. – Tea2min (talk) 06:26, 25 June 2020 (UTC)