The cohomology of pro-p groups with a powerfully embedded subgroup
نویسندگان
چکیده
منابع مشابه
THE COHOMOLOGY OF PRO-p GROUPS WITH A POWERFULLY EMBEDDED SUBGROUP
We calculate the cohomology of a pro-p group with an extendable and almost powerfully embedded subgroup. We consider the mod-p cohomology of p-groups and pro-p groups with an almost powerfully embedded subgroup satisfying an extendibility condition. The result has a strikingly simple form. If G is a pro-p group for some prime p we say that a closed, normal, finitely generated subgroup, N , is a...
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In this work, we are interested in the tame version of the Fontaine–Mazur conjecture. By viewing the pro-p-proup GS as a quotient of a Galois extension ramified at p and S, we obtain a connection between the conjecture studied here and a question of Galois structure. Moreover, following a recent work of A. Schmidt, we give some evidence of links between this conjecture, the étale cohomology and...
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let $g$ be a finite $p$-soluble group, and $p$ a sylow $p$-subgroup of $g$. it is proved that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are contained in the $k$-th term of the upper central series of $p$, then the $p$-length of $g$ is at most $2m+1$, where $m$ is the greatest integer such that $p^m-p^{m-1}leq k$, and the exponent of the image of $p$...
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let $g$ be a finite $p$-soluble group, and $p$ a sylow $p$-sub-group of $g$. it is proved that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are contained in the $k$-th term of the upper central series of $p$, then the $p$-length of $g$ is at most $2m+1$, where $m$ is the greatest integer such that $p^m-p^{m-1}leq k$, and the exponent of the image of $p$...
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This is a toy example to illustrate some of the techniques of fusion and transfer as described in Gorenstein’s text Finite Groups. Finite groups with a unique subgroup of order p (p an odd prime) are classified in terms of a cyclic p′-extension of relatively simple combinatorial data. This note is intended to address a slightly misstated exercise in somewhat more detail and to be a toy example ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2003.10.034