Cohomology and finite subgroups of profinite groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Cohomology and finite subgroups of profinite groups

Authors:	Pham Anh Minh Peter Symonds

Affiliation:	Department of Mathematics, College of Science, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam ; Department of Mathematics, U.M.I.S.T., P.O. Box 88, Manchester M60 1QD, England

Abstract:	We prove two theorems linking the cohomology of a pro- group with the conjugacy classes of its finite subgroups. The number of conjugacy classes of elementary abelian -subgroups of 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 is finite.

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