Fields with free multiplicative groups modulo torsion
نویسندگان
چکیده
منابع مشابه
On groups and fields interpretable in torsion-free hyperbolic groups
We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela’s description of imaginaries in torsion-free hy...
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The present paper is motivated by needs of practical computations in finitely presented groups. In particular, we wish to develop tools which can be used in the analysis of the “practical” complexity of algorithmic problems for discrete infinite groups, as well as in the analysis of the behaviour of heuristic (e.g. genetic) algorithms for infinite groups [22, 23]. In most computer-based computa...
متن کاملGaussian Groups Are Torsion Free
Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...
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LET G be a residually-finite torsion-free group. Is Gthe profinite completion of G-torsion free? This question was asked in [CKL] where it was shown that if G is a finitely generated metabelian-by-finite group then indeed G is torsion free. On the other hand Evans [E] showed that if G is not finitely generated then it is possible that G has torsion. His example is also metabelian. In this note ...
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We prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1980
ISSN: 0035-7596
DOI: 10.1216/rmj-1980-10-3-599