On singular equations over torsion-free groups
نویسندگان
چکیده
We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most [Formula: see text]. This result applications to equations over groups: in particular singular equation text] group solution some overgroup.
منابع مشابه
Equations over Torsion-free Groups Summary Klyachko's Methods and the Solution of Equations over Torsion-free Groups
SUMMARY The question we are concerned with here is the following : Let G be a torsion-free group and consider the free product Ghti of G with an innnite cyclic group (generator t). Let w be an element of Ghti?G and hhwii denote the normal closure of w in G hti, then is the natural homomorphism G ! G hti hhwii injective? Klyachko's paper : \Funny property of sphere and equations over groups" Kl]...
متن کاملThe adjunction problem over torsion-free groups.
We prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z.
متن کامل-torsion free Acts Over Monoids
In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general implies some other properties, respectively.
متن کاملGeometry & Topology Monographs Characterisation of a Class of Equations with Solutions over Torsion-free Groups
We study equations over torsion-free groups in terms of their \t{shape" (the occurences of the variable t in the equation). A t{shape is good if any equation with that shape has a solution. It is an outstanding conjecture 5] that all t{shapes are good. In 2] we proved the conjecture for a large class of t{shapes called amenable. In 1] Cliiord and Goldstein characterised a class of good t{shapes...
متن کاملCharacterisation of a class of equations with solutions over torsion-free groups
We study equations over torsion-free groups in terms of their “t–shape” (the occurences of the variable t in the equation). A t–shape is good if any equation with that shape has a solution. It is an outstanding conjecture [5] that all t–shapes are good. In [2] we proved the conjecture for a large class of t–shapes called amenable. In [1] Clifford and Goldstein characterised a class of good t–sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2021
ISSN: ['0218-1967', '1793-6500']
DOI: https://doi.org/10.1142/s0218196721500272