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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 27, Issue 4 (Jul 2015)

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Groups described by element numbers

Hermann Heineken
  • Department of Mathematics, University of Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
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/ Francesco G. Russo
  • Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch 7701, South Africa
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Published Online: 2013-07-05 | DOI: https://doi.org/10.1515/forum-2013-6005

Abstract

Let G be a finite group and Le(G)={xGxe=1}, where e is a positive integer dividing |G|. How do bounds on |Le(G)| influence the structure of G? Meng and Shi [Arch. Math. (Basel) 96 (2011), 109–114] have answered this question for |Le(G)|2e. We generalize their contributions, considering the inequality |Le(G)|e2 and finding a new class of groups of whose we study the structural properties.

Keywords: Metacyclic groups; Frobenius' theorem; p-groups; Sylow subgroups

MSC: 20D10; 20D15; 20D60

About the article

Received: 2013-01-08

Revised: 2013-04-03

Published Online: 2013-07-05

Published in Print: 2015-07-01


Funding Source: IMPA and UFRJ

Award identifier / Grant number: CAPES ref. no. 061/2013

Funding Source: DEIM


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-6005.

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[1]
Wei Meng
Communications in Algebra, 2017, Volume 45, Number 2, Page 660

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