Reports@SCM, Vol 3, No 1 (2017)

Explicit bounds for growth of sets in non-abelian groups

Alberto Espuny Díaz

Abstract


The Plünnecke-Ruzsa inequalities give upper bounds for the growth of iterated sumsets in an abelian group. These inequalities have been recently extended to the non-abelian case by Petridis and by Tao. The main result in this work is a proof of the non-abelian Plünnecke-Ruzsa inequalities which makes no use of the method introduced by Petridis. Analogous inequalities for iterated products of two distinct sets are also obtained.

Keywords: Additive combinatorics, combinatorial number theory, growth in groups.
MSC (2010): Primary 11B13, 11B30, 11P70. Secondary 20D60.

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ISSN: 2385-4227 (electronic edition)