Archiv der Mathematik

, Volume 77, Issue 6, pp 456–460 | Cite as

A combinatorial condition on a certain variety of groups

  • B. Taeri

Abstract.

Let n be an integer and \( \mathcal B_n \) be the variety defined by the law [xn,y][x,yn]-1 = 1.¶ Let \( \mathcal B_n^* \) be the class of groups in which for any infinite subsets X, Y there exist \( x \in X \) and \( y \in Y \) such that [xn,y][x,yn]-1 = 1. For \( n \in {\pm 2, 3\} \) we prove that¶\( \mathcal B_n^* = \mathcal B_n \cup \mathcal F \), \( \mathcal F \) being the class of finite groups. Also for \( n \in {- 3, 4\} \) and an infinite group G which has finitely many elements of order 2 or 3 we prove that \( G \in \mathcal B_n^* \) if and only if \( G \in \mathcal B_n \).

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • B. Taeri
    • 1
  1. 1.Department of Mathematics, Isfahan University of Technology, Isfahan, Iran, b.taeri@cc.iut.ac.irIR

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