On Abelian Quotients of Primitive Groups
Copyright policy )On Abelian Quotients of Primitive Groups
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 .
Primitive groups, primitive permutation group, General theory for finite permutation groups, abelian quotient, Arithmetic and combinatorial problems involving abstract finite groups
Primitive groups, primitive permutation group, General theory for finite permutation groups, abelian quotient, Arithmetic and combinatorial problems involving abstract finite groups
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