Lifting in Frattini covers and a characterization of finite solvable groups

Robert M. Guralnick; Pham Huu Tiep

doi:10.1515/crelle-2013-0085

Lifting in Frattini covers and a characterization of finite solvable groups

Robert M. Guralnick
, Pham Huu Tiep

Mathematics

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

22 Scopus citations

Abstract

We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a result of J. G. Thompson and characterize finite solvable groups as those finite groups which do not contain nontrivial elements x_i, i = 1,2,3, with x₁x₂x₃ = 1 and x_i a p_i-element for distinct primes p_i. We note some connections with coverings of curves.

Original language	English (US)
Pages (from-to)	49-72
Number of pages	24
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2015
Issue number	708
DOIs	https://doi.org/10.1515/crelle-2013-0085
State	Published - Nov 2015

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a result of J. G. Thompson and characterize finite solvable groups as those finite groups which do not contain nontrivial elements xi, i = 1,2,3, with x1x2x3 = 1 and xi a pi-element for distinct primes pi. We note some connections with coverings of curves.",

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AB - We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a result of J. G. Thompson and characterize finite solvable groups as those finite groups which do not contain nontrivial elements xi, i = 1,2,3, with x1x2x3 = 1 and xi a pi-element for distinct primes pi. We note some connections with coverings of curves.

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Lifting in Frattini covers and a characterization of finite solvable groups

Abstract

ASJC Scopus subject areas

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