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.
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