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Publicly Available Published by De Gruyter August 7, 2014

p-divisibility of conjugacy class sizes and normal p-complements

  • Antonio Beltrán EMAIL logo , María José Felipe and Changguo Shao
From the journal Journal of Group Theory

Abstract

Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of |x|G is a constant for every prime-power order element xN∖Z(N), then N is solvable and has normal p-complement.

Funding source: Valencian Government

Award Identifier / Grant number: PROMETEO/2011/30

Funding source: Spanish Government

Award Identifier / Grant number: MTM2010-19938-C03-02

Funding source: NNSF of China

Award Identifier / Grant number: 11201401

Funding source: NNSF of China

Award Identifier / Grant number: 11301218

Funding source: University of Jinan Research Funds for Doctors

Award Identifier / Grant number: XBS1335

Funding source: University of Jinan Research Funds for Doctors

Award Identifier / Grant number: XBS1336

C. G. Shao wants to express his deep gratitude for the warm hospitality he has received in the Departamento de Matemáticas of the Universidad Jaume I in Castellón, Spain.

Received: 2014-5-16
Published Online: 2014-8-7
Published in Print: 2015-1-1

© 2015 by De Gruyter

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