Class preserving automorphisms of finite p -groups
نویسندگان
چکیده
منابع مشابه
CLASS 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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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 کاملCLASS-PRESERVING AUTOMORPHISMS OF A FAMILY OF FINITE p-GROUPS
Let G be a finite p-group, p prime such that G has a normal subgroup H , there exists an element y ∈ G, y / ∈ H such that order of y is p, y ∈ ζ(G) and each element g ∈ G can be written as g = h y, h ∈ H, 1 ≤ i ≤ p, where ζ(G) denotes the center of G. It is proved that any τ ∈ Autc(G) such that for all x ∈ H , xτ = (uy)x(uy), where u is a fixed element of H and 1 ≤ i ≤ p is an inner automorphis...
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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 کاملClass Preserving Automorphisms of Blackburn Groups
In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms. 2000 Mathematics subject classification: primary 20D45; secondary 16S34.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2007
ISSN: 0024-6107
DOI: 10.1112/jlms/jdm025