Fundamental relation and automorphism group of very thin Hv-groups

Abstract

The purpose of this paper is computing the fundamental relations and automorphism groups of very thin Hv-groups. In this regards, we first investigate some basic properties of Hv-groups and then we show that any given group is isomorphic to the fundamental group of a nontrivial Hv-group. The main properties of very thin Hv-groups are also investigated and it is proved that every finite very thin Hv-group is proper.