A module-theoretic approach to abelian automorphism groups

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There are several examples in the literature of finite non-abelian p-groups whose automorphism group is abelian. For some time only examples that were special p-groups were known, until Jain and Yadav [JY12] and Jain, Rai and Yadav [JRY13] constructed several non-special examples. In this paper we show how a simple module-theoretic approach allows the construction of non-special examples, starting from special ones constructed by several authors, while at the same time avoiding further direct calculations.