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Archiv der Mathematik

, Volume 70, Issue 4, pp 257–261 | Cite as

On groups with a permutational property on commutators of weight 4

  • Chiara Nicotera
  • 33 Downloads

Abstract.

We show that a periodic 2-generator group G with no involutions is metabelian if and only if for any \( a, x_1, x_2,x_3 \in G \) there exists a nontrivial permutation \( \sigma \in \Bbb {S}_3 \) such that \( [a, x_1, x_2, x_3 ] = [a,x_{\sigma (1)},x_{\sigma (2)},x_{\sigma (3)}] \).

Keywords

Permutational Property Nontrivial Permutation 
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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Chiara Nicotera
    • 1
  1. 1.Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Complesso Universitario Monte S. Angelo – Edificio T, I-80126 Napoli, ItalyIT

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