Groups of Prime Power Order, Volume 1
14 Jan 2008-
About: The article was published on 2008-01-14. It has received 61 citations till now. The article focuses on the topics: Volume (compression).
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TL;DR: In this article, Sambale et al. showed that Brauer's k (B ) -conjecture holds for 3-blocks of defect at most 3 and for 2-blocks with minimal nonmetacyclic defect groups.
25 citations
TL;DR: The Bogomolov multiplier of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G.
Abstract: The Bogomolov multiplier of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. This invariant of G plays an important role in birational geometry of quotient spaces V/G. We show that in many cases the vanishing of the Bogomolov multiplier is guaranteed by the rigidity of G in the sense that it has no outer class-preserving automorphisms.
22 citations
TL;DR: In this article, the classification of three-generator finite p -groups with a minimal non-abelian subgroup of index p was studied, and it was shown that Φ(G )≤ Z (G ).
Abstract: This paper finishes the classification of three-generator finite p -groups G such that Φ( G )≤ Z ( G ). This paper is a part of classification of finite p -groups with a minimal non-abelian subgroup of index p , and partly solves a problem proposed by Berkovich (2008).
20 citations
TL;DR: In this paper, a complete classification of finite p-groups all of whose noncyclic subgroups are normal is given, which solves a problem stated by Berkovich and solves the problem of non-cyclical subgroups.
Abstract: We give a complete classification of finite p-groups all of whose noncyclic subgroups are normal, which solves a problem stated by Berkovich.
14 citations
TL;DR: In this article, a necessary and sufficient condition for a finite non-abelian p-group G such that Autc(G) = Autz(G), with elementary abelian or cyclic center, is given.
Abstract: Let G be a finite non-abelian p-group, where p is a prime. Let Autc(G) and Autz(G) respectively denote the group of all class preserving and central automorphisms of G. We give a necessary and sufficient condition for G such that Autc(G) = Autz(G) and classify all finite non-abelian p-groups G with elementary abelian or cyclic center such that Autc(G) = Autz(G). We also characterize all finite p-groups G of order ≤ p
7 such that Autz(G) = Autz(G) and complete the classification of all finite p-groups of order ≤ p
5 for which there exist non-inner class preserving automorphisms.
12 citations