The posets of classes of isomorphic subgroups of finite groups

Abstract

In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several particular cases it determines the structure of $G$.

accepted for publication in Bull. Malays. Math. Sci. Soc