## Illinois Journal of Mathematics

### $p$-groups of maximal class as automorphism groups

#### Abstract

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.

#### Article information

Source
Illinois J. Math., Volume 47, Number 1-2 (2003), 141-156.

Dates
First available in Project Euclid: 17 November 2009

https://projecteuclid.org/euclid.ijm/1258488144

Digital Object Identifier
doi:10.1215/ijm/1258488144

Mathematical Reviews number (MathSciNet)
MR2031311

Zentralblatt MATH identifier
1032.20024

#### Citation

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