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The classification of groups with the small squaring property on 3-sets

Published online by Cambridge University Press:  17 April 2009

P. Longobardi  and
M. Maj
P. Longobardi
Affiliation:
Dip di Matematica e Applicazioni, Università degli Studi di Napoli Monte S. Angelo, via Cinthia 80126 Naples, Italy
M. Maj
Affiliation:
Dip di Matematica e Applicazioni, Università degli Studi di Napoli Monte S. Angelo, via Cinthia 80126 Naples, Italy
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Abstract

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Let G be a group and k an integer greater than 1. We say that G has the square property of k-sets and we write G ∈ DS(k) if |X2| < k2 for any subset X of G of order k. The groups in DS(2) are exactly the Dedekind groups, as Freiman showed. The class .DS(3) has been recently studied by Berkovich, Freiman and Praeger. In this paper we complete the classification of DS(3)-groups by characterising finite 2-groups of exponent 4 in DS(3).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 263 - 270
Copyright
Copyright © Australian Mathematical Society 1992

References

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