Geodesic
FINITE $p$-GROUPS WITH SMALL AUTOMORPHISM GROUP
Forum of Mathematics, Sigma, Tome 3 (2015)

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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 $G$. 
@article{10_1017_fms_2015_6,
     author = {JON GONZ\'ALEZ-S\'ANCHEZ and ANDREI JAIKIN-ZAPIRAIN},
     title = {FINITE $p${-GROUPS} {WITH} {SMALL} {AUTOMORPHISM} {GROUP}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {3},
     year = {2015},
     doi = {10.1017/fms.2015.6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.6/}
}
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JON GONZÁLEZ-SÁNCHEZ; ANDREI JAIKIN-ZAPIRAIN. FINITE $p$-GROUPS WITH SMALL AUTOMORPHISM GROUP. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2015.6

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