Cohomology and finite subgroups of profinite groups

Minh, Pham; Symonds, Peter

doi:10.1090/S0002-9939-03-07250-2

Cohomology and finite subgroups of profinite groups
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by Pham Anh Minh and Peter Symonds

Proc. Amer. Math. Soc. 132 (2004), 1581-1588

DOI: https://doi.org/10.1090/S0002-9939-03-07250-2

Published electronically: November 4, 2003

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Abstract:

We prove two theorems linking the cohomology of a pro-$p$ group $G$ with the conjugacy classes of its finite subgroups. The number of conjugacy classes of elementary abelian $p$-subgroups of $G$ is finite if and only if the ring $H^{*}(G,\mathbb {Z}/p)$ is finitely generated modulo nilpotent elements. If the ring $H^{*}(G,\mathbb {Z} /p)$ is finitely generated, then the number of conjugacy classes of finite subgroups of $G$ is finite.

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