Talk:Green's relations
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Problem with the example?
editI was just trying to find an example of a semigroup in which all subgroups are trivial, but there exists an H-class containing more than one element..
Are you sure of yours L-class and R-class in the example? I think they are inverted... (Chaos140 (talk) 08:15, 11 February 2008 (UTC))
(Four years later...) I think the example would be correct if transformations act on the right of their arguments and are thus composed from left to right, as is customary in semigroup theory. However, the calculation below the display describing the equality of the kernel relations shows functions acting on the left of their arguments. Michael Kinyon (talk) 03:23, 28 March 2014 (UTC)
Satoh ... result
editHow does the result that there are 1,843,120,128 non-equivalent semigroups of order 8 not contradict an earlier assertion in Semi-groups that every monoid G can be embedded in the space of functions G^G ? At most there can be 9^9 semi-groups of order 8. —Preceding unsigned comment added by 92.50.71.112 (talk) 14:23, 14 April 2008 (UTC)
- I don't know all the details, but not all semigroups are monoids.Rich (talk) 22:53, 22 May 2020 (UTC)
- what i said above may not be relevant.Rich (talk) 02:00, 23 May 2020 (UTC)