A quantitative version of the non-abelian idempotent theorem

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). This is a quantitative version of the non-abelian idempotent theorem.Comment: 82 pp. Changed the title from `Indicator functions in the Fourier-Eymard algebra'. Corrected the proof of Lemma 19.1. Expanded the introduction. Corrected typo

Small cutsets in quasiminimal Cayley graphs

AbstractWe continue the recent study carried out by several authors on the cut sets in Cayley graphs with respect to quasiminimal generating sets. We improve the known results on these questions.The application of our main theorem to symmetric Cayley graphs on minimal generating sets leads to the following result.Let G be a group containing a minimal generating set M such that | M | ⩾ 4. Let S = M ∪ M−1. Then one of the following conditions holds. 1.(i) s2 = u2 and u4 = 1, for all s, u ∈ M2.(ii) For all (d + 1)-subsets A and B of G which are not of the form Γ (x) ∪ {x} for any x ∈ G, there exists d + 1 disjoint paths from A to B in Cay(G, S)