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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$.

References [Enhancements On Off] (What's this?)

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  • [AS] M. Aschbacher and L. Scott, Maximal subgroups of finite groups, J. Algebra 92 (1985), 44-80. MR 772471 (86m:20029)
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  • [I] I. M. Isaacs, Solution of problem 6523, Amer. Math. Monthly 95 (1988), 561-562. MR 1541339

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