The automorphism group of an abelian $p$-group and its normal $p$-subgroups
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- by Jutta Hausen PDF
- Trans. Amer. Math. Soc. 182 (1973), 159-164 Request permission
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 ${\mathbf {\Gamma }}$.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 182 (1973), 159-164
- MSC: Primary 20K30
- DOI: https://doi.org/10.1090/S0002-9947-1973-0325808-0
- MathSciNet review: 0325808