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.
© 2015 by De Gruyter