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An Elementary Proof That Finite Groups Lack Unique Product Structures

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
180
Issue
1
Identifiers
DOI: 10.1006/jabr.1996.0061

Abstract

Abstract A group Gis said to have a unique m-element product structure if there is a subset Sof Gsuch that the product map φ: S m → Gis a bijection. D. Dimovski (1992, J. Algebra 146, 205–209) proved using character theory that no nontrivial finite group has a unique m-element product structure for m⩾2. We provide an elementary proof of this fact.

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