SEMINAR: Groups and Combinatorics Seminar: TPP subgroup triples in finite groups

Time and place: 15:00 Friday 3 June in Weatherburn LT

Speaker: Peter Neumann (Oxford)

Title: TPP subgroup triples in finite groups

Abstract: About a dozen years ago, Henry Cohn and Christopher Umans proposed a group-theoretic attack on a famous problem in the theory of computational complexity. The problem is to pin down the exponent of matrix multiplication. Their attack involves a mixture of combinatorics and character theory of finite groups. The combinatorial side is based on what they call TPP triples of subsets of finite groups. If those subsets are subgroups $S$, $T$, $U$ then the TPP condition may be expressed simply as the condition that $S ap T$ is trivial and $ST ap U$ is trivial. I propose to give a little background, and then say a little about such triples of subgroups, focussing on finite nilpotent groups of class $2$.