Partial isomorphisms over finite fields

Abstract

In this paper, we construct a combinatorial algebra of partial isomorphisms that gives rise to a projective limit of the centers of the group algebras $\mathbb {C}\mathrm {GL}(n,\mathbb {F}_{q})$ . It allows us to prove a $\mathrm {GL}(n,\mathbb {F}_{q})$ -analogue of a theorem of Farahat and Higman regarding products of conjugacy classes of permutations.