A quantitative version of the non-abelian idempotent theorem

Abstract

Suppose that G is a finite group and A is a subset of G such that 1_A has algebra norm at most M. Then 1_A is a plus/minus sum of at most L cosets of subgroups of G, and L can be taken to be triply tower in O(M^2). This is a quantitative version of the non-abelian idempotent theorem.

83 pp. Corrected typos. Corrected Lemma 6.4 which was false as stated. The correction leads to slight weakening of the final bound

References in corpus (3)

• On a non-abelian Balog-Szemeredi-type lemma
• Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak
• On sets with small doubling

Cited by in corpus (4)

• The structure of approximate groups
• An analytic approach to a weak non-Abelian Kneser-type theorem
• Spectral theory of Fourier-Stieltjes algebras
• Noncommutative sets of small doubling