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Proceedings of the American Mathematical Society

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

 

 

Normal subgroups of groups which are products of two Abelian subgroups


Author: Larry E. Knop
Journal: Proc. Amer. Math. Soc. 40 (1973), 37-41
MSC: Primary 20F25
DOI: https://doi.org/10.1090/S0002-9939-1973-0320163-X
MathSciNet review: 0320163
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Abstract: It is shown that if a group $ G = AB$, where $ A$ and $ B$ are Abelian subgroups of $ G,A \ne B$, and either $ A$ or $ B$ satisfies the maximum condition, then there is a normal subgroup $ N$ of $ G$, $ N \ne G$, such that $ N$ contains either $ A$ or $ B$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320163-X
Keywords: Abelian subgroup, commutator subgroup, maximum condition on subgroups, metabelian groups, product of subgroups, torsion free rank, torsion subgroup
Article copyright: © Copyright 1973 American Mathematical Society