Illinois Journal of Mathematics

$p$-groups of maximal class as automorphism groups

Giovanni Cutolo, Howard Smith, and James Wiegold

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258488144

Digital Object Identifier
doi:10.1215/ijm/1258488144

Mathematical Reviews number (MathSciNet)
MR2031311

Zentralblatt MATH identifier
1032.20024

Subjects
Primary: 20F28: Automorphism groups of groups [See also 20E36]
Secondary: 20D15: Nilpotent groups, $p$-groups 20D45: Automorphisms

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


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