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

Hausen, Jutta; Schultz, Phillip

doi:10.1090/S0002-9939-98-04496-7

The maximal normal $p$-subgroup of the automorphism group of an abelian $p$-group
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by Jutta Hausen and Phillip Schultz PDF

Proc. Amer. Math. Soc. 126 (1998), 2525-2533 Request permission

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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