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Proceedings of the American Mathematical Society

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

 
 

 

The maximal normal $p$-subgroup of the automorphism group of an abelian $p$-group


Authors: Jutta Hausen and Phillip Schultz
Journal: Proc. Amer. Math. Soc. 126 (1998), 2525-2533
MSC (1991): Primary 20K10, 20F28, 20K30
DOI: https://doi.org/10.1090/S0002-9939-98-04496-7
MathSciNet review: 1458876
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Abstract: Let $p$ be a prime number and let $G$ be an abelian $p$–group. Let $\Delta$ be the maximal normal $p$–subgroup of $\operatorname {Aut}G$ and $\zeta$ the maximal $p$–subgroup of its centre. Let $\mathbf {t}$ be the torsion radical of ${\mathcal {E}}(G)$. Then $\Delta =(1+\mathbf {t})\zeta$. The result is new for $p=2$ and 3, and the proof is new and valid for all primes $p$.


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Additional Information

Jutta Hausen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email: hausen@uh.edu

Phillip Schultz
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476; Department of Mathematics, University of Western Australia, Nedlands 6009, Australia
MR Author ID: 157160
Email: schultz@maths.uwa.edu.au

Received by editor(s): January 28, 1997
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society