On Boundary Factors and Traces of Subgroups of Finite Groups

Abstract

A subgroup $E$ of a finite group $G$ is called hypercyclically embedded in $G$ if every chief factor of $G$ below $E$ is cyclic. Let $A$ be a subgroup of a group $G$. Then we call any chief factor $H/A_{G}$ of $G$ a $G$-boundary factor of $A$. For any $G$-boundary factor $H/A_{G}$ of $A$, we call the subgroup $(A\cap H)/A_{G}$ of $G/A_{G}$ a $G$-trace of $A$. On the basis of these notions, we give some new characterizations of hypercyclically embedded subgroups.

Keywords

Finite group / Hypercyclically embedded subgroup / $G$-boundary factor')">$G$-boundary factor / $G$-trace of subgroup')">$G$-trace of subgroup / Meet-irreducible subgroup