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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0994778-X
Article copyright: © Copyright 1990 American Mathematical Society