Groups with cyclic derived factor-group
Authors: Hermann Heineken, John C. Lennox, A. G. R. Stewart and James Wiegold
Journal: Proc. Amer. Math. Soc. 108 (1990), 567-568
MSC: Primary 20F05; Secondary 20D10, 20E15
MathSciNet review: 994778
Abstract: In  it is proved that a -generator metabelian group with cyclic can be generated by conjugates of a single element, and the problem was left over as to whether this is true for soluble groups in general. This paper provides counterexamples of Fitting length 3, as well as proving that the result of  is true whenever all subgroups of are subnormal.
-  J. L. Brenner, R. M. Guralnick, and James Wiegold, Two-generator groups. III, Contributions to group theory, Contemp. Math., vol. 33, Amer. Math. Soc., Providence, RI, 1984, pp. 82–89. MR 767101, https://doi.org/10.1090/conm/033/767101
-  James E. Roseblade, The permutability of orthogonal subnormal subgroups, Math. Z. 90 (1965), 365–372. MR 0186739, https://doi.org/10.1007/BF01112355