Certain extensions of \((l,m\mid n,k)\)-groups. (Q1430478)

The groups \(\langle a,b\mid a^l=b^m=(ab)^n=(ab^{-1})^k=1\rangle\) have been studied by Edjvet and Thomas in 1997. In this paper, the authors consider the extensions of zero deficiency, and deficiency 1, of such groups, and ask when these extensions are finite. For the investigation, they divide the \((l,m,n,k)\)-parameter space into eight cases (not all disjoint), and perform a coset enumeration analysis in each case, sometimes with the aid of computers and the GAP system.