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|Type:||Artigo de periódico|
|Title:||FINITENESS CONDITIONS ON SUBGROUPS OF PROFINITE p-POINCARE DUALITY GROUPS|
|Abstract:||For a prime number p let G be a profinite p-PD(n) group with a closed normal subgroup N such that G/N is a profinite p-PD(m) group and that H(i)(V,F(p)) is finite for every open subgroup V of N and all i <= [n/2]. Generalising [12, Thm. 3.7.4] we show that m <= n and N is a profinite p-PD(n-m) group. In case that G is a pro-p PD(n) group of Euler characteristic 0 with a closed normal subgroup N of type FP([n-1/2]) such that G/N is soluble-by-finite pro-p group of finite rank, we show that N is a pro-p PD(n-m) group, where m = vcd(p)(G/N). As a corollary we obtain that a pro-p PD(3) group with infinite abelianization is either soluble or contains a free nonprocyclic pro-p subgroup.|
|Editor:||Hebrew Univ Magnes Press|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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