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Publicly Available Published by De Gruyter March 10, 2015

On nilpotent and solvable quotients of primitive groups

  • Thomas Michael Keller EMAIL logo and Yong Yang
From the journal Journal of Group Theory


Extending work of Aschbacher and Guralnick on abelian quotients of finite groups, in this paper we show that if G is a primitive permutation group on a set of size n, then any nilpotent quotient of G has order at most nβ and any solvable quotient of G has order at most nα+1, where β = log 32/log 9 and α = (3 log(48) + log(24))/(3 · log(9)).

Funding source: Simons Foundation

Award Identifier / Grant number: 280770

Funding source: AMS–Simons

Award Identifier / Grant number: travel grant

The authors would like to thank the anonymous referee for a thorough reading of the manuscript.

Received: 2014-3-7
Revised: 2014-7-24
Published Online: 2015-3-10
Published in Print: 2015-7-1

© 2015 by De Gruyter

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