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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
\ …
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 …