We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
All groups considered in this paper are finite. A subgroup 
$H$ of a group 
$G$ is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of 
$G$ containing 
$H$ as a proper subgroup. He et al. [‘A note on primitive subgroups of finite groups’, Commun. Korean Math. Soc. 28(1) (2013), 55–62] proved that every primitive subgroup of 
$G$ has index a power of a prime if and only if 
$G/ \Phi (G)$ is a solvable PST-group. Let 
$\mathfrak{X}$ denote the class of groups 
$G$ all of whose primitive subgroups have prime power index. It is established here that a group 
$G$ is a solvable PST-group if and only if every subgroup of 
$G$ is an 
$\mathfrak{X}$-group.
