On abelian quotients of primitive groups-Reference-Cited by-同舟云学术

On abelian quotients of primitive groups

Published:1989 Issue:1 Volume:107 Page:89-95
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Aschbacher Michael,Guralnick Robert M.

Abstract

It is shown that if G G is a primitive permutation group on a set of size n n , then any abelian quotient of G G has order at most n n . This was motivated by a question in Galois theory. The field theoretic interpretation of the result is that if M / K M/K is a minimal extension and L / K L/K is an abelian extension contained in the normal closure of M M , then the degree of L / K L/K is at most the degree of M / K M/K .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1989-107-01/S0002-9939-1989-0982398-4/S0002-9939-1989-0982398-4.pdf

Reference5 articles.

1. M. S. Audu, Transitive permutation groups of prime-power order, Ph. D. Thesis, Oxford, 1983.

2. Maximal subgroups of finite groups;Aschbacher, M.;J. Algebra,1985

3. Generating transitive permutation groups;Kovács, L. G.;Quart. J. Math. Oxford Ser. (2),1988

4. Finite permutation groups with large abelian quotients;Kovács, L. G.;Pacific J. Math.,1989

5. Problems and Solutions: Solutions of Advanced Problems: 6523;Cantor, David G.;Amer. Math. Monthly,1988

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