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19 votes
0 answers
604 views

How is this group theoretic construct called?

Let $G$ be a finite group, $S\subset G$ a generating set, $|g| = |g|_S = $ word length with respect to $S$. Define the "defect" of $g,h$ to be $$\psi(g,h) = |g|+|h|-|gh|$$ Then $\psi:G\times G \...
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17 votes
1 answer
575 views

Group cochains invariant under the action of the symmetric group

Let $G$ be a finite group and $A$ an abelian group. Recall the cochain groups $$ C^k = \{f: G^k \to A\} $$ and the coboundary map $$ \delta : C^k \to C^{k+1} $$ $$ (\delta f)(g_1, \ldots, ...
Kevin Walker's user avatar
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8 votes
3 answers
741 views

Computations in modular cohomology of finite groups

Let $k$ be an algebraically closed field of characteristic $p$, let $G$ be a finite group whose order is divisible by $p$, and let $H(G)$ be the commutative cohomology algebra of $G$ with coefficients ...
Jared's user avatar
  • 768
7 votes
0 answers
229 views

Computation of $H^2(S_n,\mathbb{Z}/2\mathbb{Z})$

Do you have a nice modern reference where I could find the computation of $H^2(S_n,\mathbb{Z}/2\mathbb{Z})$, where the action is trivial ? I have looked at the very few books on cohomology of groups ...
GreginGre's user avatar
  • 1,766
4 votes
1 answer
189 views

cohomology of finite groups of lie type with coefficients in the adjoint module

Let $\mathbb G$ be a connected, semisimple, split group over a finite field $\mathbb F_q$ and let $G = \mathbb G(\mathbb F_q)$. Let $\mathfrak g$ be its Lie algebra, an $\mathbb F_q$-vector space with ...
user94041's user avatar
  • 391