The depth of subgroups of PSL(2,q) II

This paper continues Fritzsche (2012) [4], where the ordinary depths of the subgroups of G:=PSL(2,q) with q a prime power are determined. Now, we will pay attention to the minimal combinatorial depths of the subgroups of G. It turns out that most of the subgroups have a minimal combinatorial depth ⩽7, and often it coincides with the ordinary depth of this subgroup in G. However, if H⩽G is of order pf−1, where q=pf with p a prime and f⩾3, then H has minimal combinatorial depth 2f−2 in G, and the normalizer of H in G has minimal combinatorial depth 2f−1 in G.