On τ-Closed Formations of n-Ary Group

Abstract

We prove that if G is a nonsingle-element n-ary finite group that belongs to a τ-closed formation $\mathfrak{F}$, then $G/{\text{soc(}}G{\text{)}} \in \Phi _\tau (\mathfrak{F})$, where $\Phi _\tau (\mathfrak{F})$ is the intersection of all maximal τ-closed subformations of the τ-closed formation of n-ary groups $\mathfrak{F}$.