Groups with cyclic derived factor-group
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- by Hermann Heineken, John C. Lennox, A. G. R. Stewart and James Wiegold PDF
- Proc. Amer. Math. Soc. 108 (1990), 567-568 Request permission
Abstract:
In [1] it is proved that a $k$-generator metabelian group with $G/G’$ cyclic can be generated by $k$ 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 [1] is true whenever all subgroups of $G’$ are subnormal.References
- 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, DOI 10.1090/conm/033/767101
- James E. Roseblade, The permutability of orthogonal subnormal subgroups, Math. Z. 90 (1965), 365–372. MR 186739, DOI 10.1007/BF01112355
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 567-568
- MSC: Primary 20F05; Secondary 20D10, 20E15
- DOI: https://doi.org/10.1090/S0002-9939-1990-0994778-X
- MathSciNet review: 994778