A note on basic free modules and the condition.
Marcelo, Agustín, Marcelo, Félix, Rodríguez, César (2006)
Portugaliae Mathematica. Nova Série
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Marcelo, Agustín, Marcelo, Félix, Rodríguez, César (2006)
Portugaliae Mathematica. Nova Série
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Martin Evans (2014)
Open Mathematics
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Let F n denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ F m ↠ G and S ↪ F m ↠ G are presentations of G and let and denote the associated relation modules of G. It is well known that even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G...
Radoslav M. Dimitrić (1987)
Czechoslovak Mathematical Journal
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R. Göbel, B. Goldsmith (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Lorenzo Robbiano (1979)
Compositio Mathematica
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Wolfson, Kenneth G. (1990)
Portugaliae mathematica
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Pengelley, David J., Williams, Frank (2003)
Algebraic & Geometric Topology
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Micheal N. Dyer (1978)
Compositio Mathematica
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Ian J. Leary, Brita E. A. Nucinkis (2001)
Publicacions Matemàtiques
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We give homological conditions on groups such that whenever the conditions hold for a group G, there is a bound on the orders of finite subgroups of G. This extends a result of P. H. Kropholler. We also suggest a weaker condition under which the same conclusion might hold.