Is there a name for the family of groups given by $n$ generators ($g_1, g_2,\ldots g_n$) and the following relations?
$$g_ig_jg_i = g_jg_ig_j,~\forall i,j \in \lbrace 1,\ldots n\rbrace,~i\neq j\\ g_ig_i = 1,\forall i \in \lbrace 1,\ldots n \rbrace $$
The relations are quite similar to the ones for a braid group, but then the first relation holds between any pair of generators and the generators are self-inverse.
Is there a name for this family of groups?