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ON VANISHING CRITERIA THAT CONTROL FINITE GROUP STRUCTURE II

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 August 2018

JULIAN BROUGH Open the ORCID record for JULIAN BROUGH [Opens in a new window]  and
QINGJUN KONG Open the ORCID record for QINGJUN KONG [Opens in a new window]
JULIAN BROUGH*
Affiliation:
Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany email julian.m.a.brough@gmail.com
QINGJUN KONG
Affiliation:
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, PR China email kqj2929@163.com
*
✉julian.m.a.brough@gmail.com
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Abstract

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The first author [J. Brough, ‘On vanishing criteria that control finite group structure’, J. Algebra458 (2016), 207–215] has shown that for certain arithmetical results on conjugacy class sizes it is enough to consider only the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only vanishing elements of prime power order.

Keywords

vanishing conjugacy classessoluble groupssupersoluble groups

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Secondary: 20D06: Simple groups 20D08: Simple groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 251 - 257
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author gratefully acknowledges financial support by the ERC Advanced Grant 291512 and the Alexander von Humboldt Fellowship for Postdoctoral Researchers. The research of the second author is supported by the National Natural Science Foundation of China (11301378).

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