A refinement on a theorem of Z. Janko

Abstract

We say that a subgroup $H$ is isolated in a group $G$ if for each $x\in G$ we have either $x\in H$ or $\langle x\rangle \cap H={1}$. Z. Janko, in his paper [J. Algebra, 465(2016), 41--61], determined certain classes of finite nonabelian $p$-groups which possess some isolated subgroups. In this note, a theorem of his paper is refined.