Cauchy-Davenport theorem in group extensions

Karolyi, Gyula (2005) Cauchy-Davenport theorem in group extensions. L'Enseignement Mathematique, 51 239-254. doi:10.5169/seals-3597


Author Karolyi, Gyula
Title Cauchy-Davenport theorem in group extensions
Journal name L'Enseignement Mathematique   Check publisher's open access policy
ISSN 0013-8584
Publication date 2005
Sub-type Article (original research)
DOI 10.5169/seals-3597
Volume 51
Start page 239
End page 254
Total pages 16
Place of publication Carouge, Switzerland
Publisher Universite de Geneve
Language eng
Abstract Let A and B be nonempty subsets of a finite group G in which the order of the smallest nontrivial subgroup is not smaller than d=|A|+|B|-1. Then the product set AB has at least d elements. This extends a classical theorem of Cauchy and Davenport to noncommutative groups. We also generalize Vosper's inverse theorem in the same spirit, giving a complete description of the critical pairs. The proofs depend on the structure of group extensions.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Thu, 23 Feb 2012, 16:05:20 EST by Kay Mackie on behalf of School of Mathematics & Physics