Centralizers of coprime automorphisms of finite groups
نویسندگان
چکیده
منابع مشابه
Finite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
متن کاملFinite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
متن کاملFinite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملCentralizers in Locally Finite Groups
The topic of the present paper is the following question. Let G be a locally finite group admitting an automorphism φ of finite order such that the centralizer CG(φ) satisfies certain finiteness conditions. What impact does this have on the structure of the group G? Equivalently, one can ask the same question when φ is an element of G. Sometimes the impact is quite strong and the paper is a sur...
متن کاملA Note on Absolute Central Automorphisms of Finite $p$-Groups
Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 2012
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-012-0274-x