Let Δ(G) denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which G/Δ(G) is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.
Digital Object Identifier (DOI)
Ballester-Bolinches, Adolfo; Beidleman, James C.; Heineken, Hermann; Ragland, Matthew F.; and Schmidt, Jack, "On the Intersection of Certain Maximal Subgroups of a Finite Group" (2014). Mathematics Faculty Publications. 11.