DERIVED SUBGROUPS OF PRODUCTS OF AN ABELIAN AND A CYCLIC SUBGROUP
Marston Conder, I. Martin Isaacs · Journal of the London Mathematical Society · 2004
Let G be a finite group and suppose that G = AB, where A and B are abelian subgroups. By a theorem of Ito, the derived subgroup G′ is known to be abelian. If either of the subgroups A or B is cyclic, then more can be said. The paper shows, for example, that G′/(G′∩A) is isomorphic to a subgroup of B in this case.