Finite and locally solvable periodic groups with given intersections of certain subgroups

Abstract

Let G be a group and p be a prime. We say that two subgroups $H, K$ are incident if either $H ∩ K = H$ or $H∩ K = K$. A group G is an $IC_p$-group if, for any finite non-incident subgroups $H, K$ of G, a p-Sylow subgroup of $H ∩ K$ is cyclic. In this paper we give a complete classification of solvable and locally solvable periodic $IC_p$-groups.