Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 47, Number 1-2 (2003), 141-156.
$p$-groups of maximal class as automorphism groups
We classify the (finite) $p$-groups of maximal class that are isomorphic to the full automorphism group of a (finite or infinite) group. The only such $p$-groups are the nonabelian groups of order $8$ and 3-groups in a certain family, whose structure is fully described. Up to isomorphism there is exactly one such 3-group for each even nilpotency class greater than $2$, and none for other classes.
Illinois J. Math., Volume 47, Number 1-2 (2003), 141-156.
First available in Project Euclid: 17 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F28: Automorphism groups of groups [See also 20E36]
Secondary: 20D15: Nilpotent groups, $p$-groups 20D45: Automorphisms
Cutolo, Giovanni; Smith, Howard; Wiegold, James. $p$-groups of maximal class as automorphism groups. Illinois J. Math. 47 (2003), no. 1-2, 141--156. doi:10.1215/ijm/1258488144. https://projecteuclid.org/euclid.ijm/1258488144