Automorphisms which centralize a Sylow p-subgroup
نویسندگان
چکیده
منابع مشابه
on $p$-soluble groups with a generalized $p$-central or powerful sylow $p$-subgroup
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 $p$...
متن کاملon p-soluble groups with a generalized p-central or powerful sylow p-subgroup
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 $p$...
متن کاملAutomorphisms of principal blocks stabilizing Sylow subgroups
Let p be a prime,G a finite group which has a normal p-subgroup containing its own centralizer inG, and R a commutative local ring with residue class field of characteristic p. In this paper, it is shown that if α is an augmented automorphism of RG which fixes a Sylow p-subgroup P of G, there is ρ ∈ Aut(G) such that xαρ = x for all x ∈ P , and αρ is an inner automorphism of RG.
متن کاملOn Marginal Automorphisms of a Group Fixing the Certain Subgroup
Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
متن کاملA representation of the p-sylow subgroup of Perm(Fpn) and a cryptographic application
This article concerns itself with the triangular permutation group, induced by triangular polynomial maps over Fp, which is a p-sylow subgroup of Perm(Fp ). The aim of this article is twofold: on the one hand, we give an alternative to Fp-actions on Fp , namely Z-actions on Fp and how to describe them as what we call “Z-flows”. On the other hand, we describe how the triangular permutation group...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1982
ISSN: 0021-8693
DOI: 10.1016/0021-8693(82)90287-3