On a family of groups defined by Said Sidki

In a paper in 1982, Said Sidki defined a 2-parameter family of finitely presented groups Y(m,n) that generalise the Carmichael presentation for a finite alternating group satisfied by its generating 3-cycles (1,2,t) for t⩾3. For m⩾2 and n⩾2, the group Y(m,n) is the abstract group generated by elements a1,a2,⋯,am subject to the defining relations ain=1 for 1⩽i⩽m and (aikajk)2=1 for 1⩽i