Some properties of a permutation representation of a group by cosets to its included subgroups

Abstract

Theorem 1. Let G be a group and H ⊆ K ⊆ G be its two included subgroups. Let set T = {ti, j}i∈E1, j∈E2 be a loop transversal in G to H and set T1 = {t0, j}j∈E2 be a corresponding loop transversal in K to H.