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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The automorphism group of an abelian $ p$-group and its normal $ p$-subgroups


Author: Jutta Hausen
Journal: Trans. Amer. Math. Soc. 182 (1973), 159-164
MSC: Primary 20K30
MathSciNet review: 0325808
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Abstract: Let $ {\mathbf{\Gamma }}$ be the automorphism group of a nonelementary reduced abelian p-group, $ p \geq 5$. It is shown that every noncentral normal subgroup of $ {\mathbf{\Gamma }}$ contains a noncentral normal subgroup $ {\mathbf{\Delta }}$ of $ {\mathbf{\Gamma }}$ such that $ {{\mathbf{\Delta }}^p} = 1$. Furthermore, every cyclic normal subgroup of $ {\mathbf{\Gamma }}$ is contained in the center of $ {\mathbf{\Gamma }}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0325808-0
PII: S 0002-9947(1973)0325808-0
Keywords: Abelian p-group, automorphism group, normal subgroups of automorphism groups
Article copyright: © Copyright 1973 American Mathematical Society