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Questions about the branch of algebra that deals with groups.

1 vote
0 answers
150 views

Isomorphism in homology

I asked this question on Mathematics SE three days ago, but didn't get the answer. $\require{AMScd}$Let $G, H, K$ be groups and suppose that we have a diagram $$\begin{CD} G @>f_1>> H\\ @Vg_1VV\\ K \ …
Fat ninja's user avatar
  • 403
10 votes
1 answer
664 views

Cohomology of simple finite groups remembers the group?

Let $G$ and $H$ be finite simple groups. I expect that if $G$ and $H$ are not isomorphic, then their cohomology groups with integral coefficients are not all isomorphic, that is, $H^*(G,\mathbb{Z …
Fat ninja's user avatar
  • 403