Fundamental relation and automorphism group of very thin Hv-groups

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