On the critical pair theory in abelian groups: Beyond Chowla’s Theorem

Abstract

We obtain critical pair theorems for subsets S and T of an abelian group such that |S + T| ≤ |S| + |T|. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rødseth and one of the authors.

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Correspondence to Oriol Serra.

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Supported by the Spanish Research Council under project MTM2005-08990-C02-01 and by the Catalan Research Council under project 2005SGR00256.

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Hamidoune, Y.O., Serra, O. & Zémor, G. On the critical pair theory in abelian groups: Beyond Chowla’s Theorem. Combinatorica 28, 441 (2008). https://doi.org/10.1007/s00493-008-2262-8

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Mathematics Subject Classification (2000)

  • 11P70