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Questions about the branch of algebra that deals with groups.

4 votes
Accepted

Tate Cohomology via stable categories

To address Hanno's question about checking that composition gives a graded-commutative ring structure on $End^{*}(\mathbb{Z}) = \oplus_i [\mathbb{Z}, \Omega^{-i} \mathbb{Z}]$ suppose first that $a \st …
Greg Stevenson's user avatar
2 votes

Separators in the Category of Groups

It is the minimal separator in the sense that it corepresents the forgetful functor Grp $\rightarrow$ Set, but this uses sets so probably isn't what you are after. In fact it is the same as the statem …
Greg Stevenson's user avatar
5 votes

When does "splits" imply "cosplits"?

So the fact that you had a hard time thinking of cosplit sequences of groups and the last question got me thinking (along the lines of Joel's comment actually)... what I came up with is probably stand …
Greg Stevenson's user avatar
49 votes
Accepted

Order of an automorphism of a finite group

Yes every automorphism has order bounded by |G|-1, provided G is not the trivial group. A reference is M V Horoševskiĭ 1974 Math. USSR Sb. 22 584-594 which can be found at http://www.iop.org/EJ/abstra …
Greg Stevenson's user avatar