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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Online
ISSN
1435-4446
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Volume 17, Issue 1

Issues

Groups with strongly p-embedded subgroups and cyclic Sylow p-subgroups

Hy Ginsberg
Published Online: 2013-09-20 | DOI: https://doi.org/10.1515/jgt-2013-0039

Abstract.

We establish necessary conditions under which is contained in a unique maximal subgroup H for a cyclic Sylow p-subgroup P of a quasisimple group G. We then use these results to establish necessary and in most cases sufficient conditions for the special case in which H is a p-local subgroup. Groups satisfying these hypotheses (including the p-local hypothesis) are precisely the groups possessing unfaithful minimal Heilbronn characters, and are relevant to the study of Artin's conjecture on the holomorphy of L-series. Moreover, since in this case is necessarily strongly p-embedded in G, this work complements existing results pertaining to strongly p-embedded subgroups of groups with noncyclic Sylow p-subgroups.

About the article

Received: 2012-08-04

Revised: 2012-11-05

Published Online: 2013-09-20

Published in Print: 2014-01-01


Citation Information: Journal of Group Theory, Volume 17, Issue 1, Pages 175–190, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2013-0039.

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