Class-preserving automorphisms and the normalizer property for Blackburn groups
نویسندگان
چکیده
منابع مشابه
Class-preserving Automorphisms and the Normalizer Property for Blackburn Groups
For a group G, let U be the group of units of the integral group ring ZG. The group G is said to have the normalizer property if NU (G) = Z(U)G. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being nontrivial. Groups G for which class-preserving automorphisms are inner automorphism...
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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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^...
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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.
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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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2009
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2008.068