منابع مشابه
A 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.
متن کاملON AUTOMORPHISMS OF SOME FINITE p-GROUPS
We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Autc(G) = Inn(G), where Autc(G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Autc(G) ∼= Autc(H). Finally we study class preserving automorphisms of groups o...
متن کاملOn equality of absolute central and class preserving automorphisms of finite $p$-groups
Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...
متن کاملOuter Automorphisms of Locally Finite p-Groups∗
Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].
متن کاملCLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS
We classify all finite p-groups G for which |Autc(G)| attains its maximum value, where Autc(G) denotes the group of all class preserving automorphisms of G.
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2007
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2007.064