The Divisible and E-Injective Hulls of a Torsion Free Group

1984 ◽  
pp. 163-179 ◽  
Author(s):  
C. Vinsonhaler
Keyword(s):  
Free Group ◽  
Torsion Free Group ◽  
Injective Hulls ◽  
Torsion Free

scholarly journals A just-nonsolvable torsion-free group defined on the binary tree

1999 ◽  
Vol 211 (1) ◽  
pp. 99-114 ◽  
Author(s):  
A.M. Brunner ◽  
Said Sidki ◽  
Ana Cristina Vieira
Keyword(s):  
Free Group ◽  
Binary Tree ◽  
Torsion Free Group ◽  
Torsion Free

scholarly journals On a Nonsingular Equation of Length 9 Over Torsion Free Groups

2019 ◽  
Vol 12 (2) ◽  
pp. 590-604
Author(s):  
M. Fazeel Anwar ◽  
Mairaj Bibi ◽  
Muhammad Saeed Akram
Keyword(s):  
Free Group ◽  
Free Groups ◽  
Torsion Free Group ◽  
Torsion Free

In \cite{levin}, Levin conjectured that every equation is solvable over a torsion free group. In this paper we consider a nonsingular equation $g_{1}tg_{2}t g_{3}t g_{4} t g_{5} t g_{6} t^{-1} g_{7} t g_{8}t \\ g_{9}t^{-1} = 1$ of length $9$ and show that it is solvable over torsion free groups modulo some exceptional cases.

scholarly journals Abelian groups with small cotorsion images

1991 ◽  
Vol 50 (2) ◽  
pp. 243-247 ◽  
Author(s):  
Rüdiger Göbel
Keyword(s):  
Homomorphic Image ◽  
Free Group ◽  
Abelian Groups ◽  
Torsion Free Group ◽  
Compact Abelian Groups ◽  
Torsion Free

AbstractEpimorphic images of compact (algebraically compact) abelian groups are called cotorsion groups after Harrison. In a recent paper, Ph. Schultz raised the question whether “cotorsion” is a property which can be recognized by its small cotorsion epimorphic images: If G is a torsion-free group such that every torsion-free reduced homomorphic image of cardinality is cotorsion, is G necessarily cortorsion? In this note we will give some counterexamples to this problem. In fact, there is no cardinal k which is large enough to test cotorsion.

scholarly journals ON THE ASPHERICITY OF LENGTH-6 RELATIVE PRESENTATIONS WITH TORSION-FREE COEFFICIENTS

2008 ◽  
Vol 51 (1) ◽  
pp. 201-214
Author(s):  
Seong Kun Kim
Keyword(s):  
Free Group ◽  
Zero Divisor ◽  
Point Of View ◽  
Torsion Free Group ◽  
Torsion Free

AbstractAn interesting result of Ivanov implies that a non-aspherical relative presentation that defines a torsion-free group would provide a potential counterexample to the Kaplansky zero-divisor conjecture. In this point of view, we prove the asphericity of the length-6 relative presentation $\langle H,x: xh_1xh_2xh_3xh_4xh_5xh_6\rangle$, provided that each coefficient is torsion free.

Periodic cohomology and subgroups with bounded Bredon cohomological dimension

2008 ◽  
Vol 144 (2) ◽  
pp. 329-336 ◽  
Author(s):  
JANG HYUN JO ◽  
BRITA E. A. NUCINKIS
Keyword(s):  
Free Group ◽  
Amenable Group ◽  
Cohomological Dimension ◽  
Dimensional Model ◽  
Torsion Free Group ◽  
Bredon Cohomology ◽  
Finite Dimensional ◽  
Torsion Free

AbstractMislin and Talelli showed that a torsion-free group in$\HF$with periodic cohomology after some steps has finite cohomological dimension. In this note we look at similar questions for groups with torsion by considering Bredon cohomology. In particular we show that every elementary amenable group acting freely and properly on some$\R^n$×Smadmits a finite dimensional model for$\E$G.

scholarly journals Torsion-free group without unique product property

1987 ◽  
Vol 108 (1) ◽  
pp. 116-126 ◽  
Author(s):  
Eliyahu Rips ◽  
Yoav Segev
Keyword(s):  
Free Group ◽  
Torsion Free Group ◽  
Product Property ◽  
Unique Product ◽  
Torsion Free

scholarly journals The power graph of a torsion-free group

2018 ◽  
Vol 49 (1) ◽  
pp. 83-98 ◽  
Author(s):  
Peter J. Cameron ◽  
Horacio Guerra ◽  
Šimon Jurina
Keyword(s):  
Free Group ◽  
Torsion Free Group ◽  
Power Graph ◽  
Torsion Free

An independence theorem for automorphisms of torsion-free groups

1981 ◽  
Vol 90 (3) ◽  
pp. 403-409
Author(s):  
U. H. M. Webb
Keyword(s):  
Automorphism Group ◽  
Nilpotent Group ◽  
Free Group ◽  
Automorphism Groups ◽  
Torsion Free Group ◽  
Free Nilpotent Group ◽  
Free Abelian Groups ◽  
Independence Theorem ◽  
The Relationship ◽  
Torsion Free

This paper considers the relationship between the automorphism group of a torsion-free nilpotent group and the automorphism groups of its subgroups and factor groups. If G2 is the derived group of the group G let Aut (G, G2) be the group of automorphisms of G which induce the identity on G/G2, and if B is a subgroup of Aut G let B¯ be the image of B in Aut G/Aut (G, G2). A p–group or torsion-free group G is said to be special if G2 coincides with Z(G), the centre of G, and G/G2 and G2 are both elementary abelian p–groups or free abelian groups.

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