On a combinatorial problem in group theory

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Research output: Contribution to journalArticlepeer-review

Abstract

We say that a group G ∈DS if for some integer m, all subsets X of G of size m satisfy |X 2|<|X|2, where X 2={xy|x,y ∈X}. It is shown, using a previous result of Peter Neumann, that G ∈DS if and only if either the subgroup of G generated by the squares of elements of G is finite, or G contains a normal abelian subgroup of finite index, on which each element of G acts by conjugation either as the identity automorphism or as the inverting automorphism.

Original languageEnglish
Pages (from-to)329-340
Number of pages12
JournalIsrael Journal of Mathematics
Volume82
Issue number1-3
DOIs
StatePublished - Jun 1993

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