Finite p-groups with small automorphism group

Jon Gonzalez-Sanchez; Andrei Jaikin-Zapirain

Finite p-groups with small automorphism group

Group Theory 2014-06-25 v2

Authors: Jon Gonzalez-Sanchez , Andrei Jaikin-Zapirain

Abstract

For each prime $p$ we construct a family $\{G_i\}$ of finite $p$ -groups such that $|\Aut (G_i)|/|G_i|$ goes to $0$ , as $i$ goes to infinity. This disproves a well-known conjecture that $|G|$ divides $|\Aut(G)|$ for every non-abelian finite $p$ -group $G$ .

Keywords

finite groups finite group theory group theory

Cite

@article{arxiv.1406.5772,
  title  = {Finite p-groups with small automorphism group},
  author = {Jon Gonzalez-Sanchez and Andrei Jaikin-Zapirain},
  journal= {arXiv preprint arXiv:1406.5772},
  year   = {2014}
}

Comments

8 pages

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