On subgroups containing non-trivial normal subgroups

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2003 Italy English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 137, pages 183-188 (issn: 0021-2172, eissn: 1565-8511,

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Authors: HERZOG M.; KAPLAN G.; LUCCHINI, ANDREA;

doi: 10.1007/bf02785961

handle: 11577/127389

On subgroups containing non-trivial normal subgroups

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Abstract

We prove that ifA≠1 is a subgroup of a finite groupG and the order of an element in the centralizer ofA inG is strictly larger (larger or equal) than the index [G:A], thenA contains a non-trivial characteristic (normal) subgroup ofG. Consequently, ifA is a stabilizer in a transitive permutation group of degreem>1, thenexp(Z(A))

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Italy

Related Organizations

University of Padua
Italy
Tel Aviv University
Israel
Academic College of Tel Aviv-Yafo
Israel

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