On the cardinality of set products in groups
Richard D. Byrd, Justin T. Lloyd, James W. Stepp (1980)
Colloquium Mathematicae
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Richard D. Byrd, Justin T. Lloyd, James W. Stepp (1980)
Colloquium Mathematicae
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Georges Skandalis, Thierry Fack (1981)
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Mladen Bestvina, Mark Feighn (1995)
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Garzón, Antonio, Inassaridze, Hvedri (2001)
Homology, Homotopy and Applications
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G. Malle, Gerhard Hiss, Frank Lübeck (1995)
Manuscripta mathematica
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S.M. Gersten, H.B. Short (1990)
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Ana Agore, Gigel Militaru (2012)
Open Mathematics
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We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ...
Stephen G. Brick (1988)
Inventiones mathematicae
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Richard Weiss, John van Bon (1992)
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A. Marden, B. Maskit (1979)
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Jérémie Brieussel (2014)
Annales de l’institut Fourier
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An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
M. Yamasaki (1987)
Inventiones mathematicae
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