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Results tagged with finite-groups
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user 510150
Questions on group theory which concern finite groups.
9
votes
Regular orbits for automorphisms of finite simple groups
As pointed out by Michael Giudici the answer is given by a result of Horoševskiĭ. Here is a proof following the paper by Horoševskiĭ.
Lemma: Let $\phi$ be an automorphism of $G$ with $|\phi|$ divisib …
- 884
13
votes
1
answer
408
views
Number of finite groups: is $\operatorname{gnu}(4n) \geq 2 \operatorname{gnu}(n)$?
Let $\operatorname{gnu}(n)$ be the number of finite groups of order $n$.
Question: Is it true that $\operatorname{gnu}(4n) \geq 2 \operatorname{gnu}(n)$ for all $n \geq 1$?
Surely this must be true, …
- 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