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FINITE $p$-GROUPS WITH SMALL AUTOMORPHISM GROUP
Published online by Cambridge University Press: 20 April 2015
Abstract
For each prime $p$ we construct a family $\{G_{i}\}$ of finite $p$-groups such that $|\text{Aut}(G_{i})|/|G_{i}|$ tends to zero as $i$ tends to infinity. This disproves a well-known conjecture that $|G|$ divides $|\text{Aut}(G)|$ for every nonabelian finite $p$-group $G$.
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- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Author(s) 2015
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