This article is cited in 9 papers

$k$-Free-like groups

A. Yu. Olshanskii^ab, M. V. Sapir<sup>b

a</sup> Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
^b Dep. Math., Vanderbilt Univ., Nashville, TN, USA

Abstract: The following results are proved.
In Theorem 1, it is stated that there exist both finitely presented and not finitely presented 2-generated nonfree groups which are $k$-free-like for any $k\ge2$.
In Theorem 2, it is claimed that every nonvirtually cyclic (resp., noncyclic and torsion-free) hyperbolic $m$-generated group is $k$-free-like for every $k\ge m+1$ (resp., $k\ge m$).
Finally, Theorem 3 asserts that there exists a 2-generated periodic group $G$ which is $k$-free-like for every $k\ge3$.

Keywords: $k$-free-like groups.

UDC: 512.5

Received: 17.11.2008

 English version: Algebra and Logic, 2009, 48:2, 140–146

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