Power sets and soluble subgroups

Martin W. Liebeck; Aner Shalev

doi:10.1090/S0002-9939-2014-12203-9

Power sets and soluble subgroups

Martin W. Liebeck, Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for certain positive integers k, such as 12, a normal subgroup of a finite group which consists of k^th powers is necessarily soluble. This gives rise to new solubility criteria, and solves an open problem from a 2013 paper by the authors.

Original language	English
Pages (from-to)	3757-3760
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	142
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2014-12203-9
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2014-12203-9

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title = "Power sets and soluble subgroups",

abstract = "We prove that for certain positive integers k, such as 12, a normal subgroup of a finite group which consists of kth powers is necessarily soluble. This gives rise to new solubility criteria, and solves an open problem from a 2013 paper by the authors.",

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DO - 10.1090/S0002-9939-2014-12203-9

M3 - مقالة

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SP - 3757

EP - 3760

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Power sets and soluble subgroups

Abstract

All Science Journal Classification (ASJC) codes

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