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This article is cited in 9 scientific papers (total in 9 papers)
$k$-Free-like groups
A. Yu. Olshanskiiab, M. V. Sapirb a 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.
Received: 17.11.2008
Citation:
A. Yu. Olshanskii, M. V. Sapir, “$k$-Free-like groups”, Algebra Logika, 48:2 (2009), 245–257; Algebra and Logic, 48:2 (2009), 140–146
Linking options:
https://www.mathnet.ru/eng/al398 https://www.mathnet.ru/eng/al/v48/i2/p245
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Abstract page: | 507 | Full-text PDF : | 124 | References: | 54 | First page: | 11 |
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