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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On abelian quotients of primitive groups


Authors: Michael Aschbacher and Robert M. Guralnick
Journal: Proc. Amer. Math. Soc. 107 (1989), 89-95
MSC: Primary 20B05; Secondary 12F05, 20B25, 20B35
MathSciNet review: 982398
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Abstract: It is shown that if $ G$ is a primitive permutation group on a set of size $ n$, then any abelian quotient of $ G$ has order at most $ n$. This was motivated by a question in Galois theory. The field theoretic interpretation of the result is that if $ M/K$ is a minimal extension and $ L/K$ is an abelian extension contained in the normal closure of $ M$, then the degree of $ L/K$ is at most the degree of $ M/K$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0982398-4
Article copyright: © Copyright 1989 American Mathematical Society