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Results tagged with group-cohomology
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user 510150
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
0
votes
Explicit $2$-cocycle for $2^{1+2n}_+$
The extraspecial group $P = 2_{+}^{1+2n}$ has generators $z$, $v_1$, $\ldots$, $v_n$, $w_1$, $\ldots$, $w_n$, with $Z(P) = \langle z \rangle$ cyclic of order $2$ and
\begin{align*}
v_i^2 = w_i^2 = 1 & …
- 884
5
votes
1
answer
289
views
Extension of base field for modules of groups and cohomology [duplicate]
Let $G$ be a group and let $K/k$ be a field extension. Suppose that $V$ is a $kG$-module, and let $V_K = K \otimes_k V$ be the $KG$-module given by changing the base field.
Is it true that $H^n(G,V_K) …
- 884