Partial isomorphisms over finite fields
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.
combinatorics over finite fields linear groups ivanovkerov algebra