A criterion for metanilpotency of a finite group (original) (raw)

Abstract

We prove that the kth term of the lower central series of a finite group G is nilpotent if and only if {|ab|=|a||b|} for any {\gamma_{k}} -commutators {a,b\in G} of coprime orders.

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References (6)

  1. R. Bastos and P. Shumyatsky, A Sufficient Condition for Nilpotency of the Commutator Subgroup, Siberian Mathematical Journal, 57 (2016), 762-763.
  2. B. Baumslag and J. Wiegold, A Sufficient Condition for Nilpotency in a Finite Group, preprint available at arXiv:1411.2877v1 [math.GR].
  3. D. Gorenstein, Finite Groups, Chelsea Publishing Company, New York, 1980.
  4. M. Kassabov and N. Nikolov, Words with few values in finite simple groups, The Quarterly Journal of Mathematics, 64 (2013), 1161-1166.
  5. D.J.S. Robinson, A Course in the Theory of Groups, 2nd Edition, Springer- Verlag, 1995.
  6. A. Turull, Fitting height of groups and of fixed points, Journal of Algebra, 86 (1984), 555-566.