scholarly journals Abelian JSJ decomposition of graphs of free abelian groups

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Benjamin Beeker
Keyword(s):  
Abelian Groups ◽  
Jsj Decomposition ◽  
Free Abelian Groups

Abstract.A group

scholarly journals COMPATIBILITY JSJ DECOMPOSITION OF GRAPHS OF FREE ABELIAN GROUPS

2013 ◽  
Vol 23 (08) ◽  
pp. 1837-1880
Author(s):  
BENJAMIN BEEKER
Keyword(s):  
Abelian Groups ◽  
Finite Graph ◽  
Finitely Generated ◽  
Graph Of Groups ◽  
Jsj Decomposition ◽  
Free Abelian Groups

A group G is a v GBS group if it admits a decomposition as a finite graph of groups with all edge and vertex groups finitely generated and free abelian. We describe the compatibility JSJ decomposition over abelian groups. We prove that in general this decomposition is not algorithmically computable.

On the square subgroups of decomposable torsion-free abelian groups of rank three

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Fysal Hasani ◽  
Fatemeh Karimi ◽  
Alireza Najafizadeh ◽  
Yousef Sadeghi
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

AbstractThe square subgroup of an abelian group

Direct decompositions of torsion-free Abelian groups of finite rank

1985 ◽  
Vol 30 (1) ◽  
pp. 1803-1810
Author(s):  
E. A. Blagoveshchenskaya
Keyword(s):  
Finite Rank ◽  
Abelian Groups ◽  
Free Abelian Groups ◽  
Direct Decompositions ◽  
Torsion Free

On the SL(2, C)-representation rings of free abelian groups

2018 ◽  
Vol 167 (02) ◽  
pp. 229-247
Author(s):  
TAKAO SATOH
Keyword(s):  
Abelian Group ◽  
Upper Bound ◽  
Automorphism Groups ◽  
Free Abelian Group ◽  
Abelian Groups ◽  
Free Groups ◽  
The Other ◽  
Subsequent Research ◽  
Representation Rings ◽  
Free Abelian Groups

AbstractIn this paper, we study “the ring of component functions” of SL(2, C)-representations of free abelian groups. This is a subsequent research of our previous work [11] for free groups. We introduce some descending filtration of the ring, and determine the structure of its graded quotients.Then we give two applications. In [30], we constructed the generalized Johnson homomorphisms. We give an upper bound on their images with the graded quotients. The other application is to construct a certain crossed homomorphisms of the automorphism groups of free groups. We show that our crossed homomorphism induces Morita's 1-cocycle defined in [22]. In other words, we give another construction of Morita's 1-cocyle with the SL(2, C)-representations of the free abelian group.

Basic subgroups and a freeness criterion for torsion-free abelian groups

1999 ◽  
pp. 247-255 ◽  
Author(s):  
Andreas Blass ◽  
John Irwin
Keyword(s):  
Abelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO

2006 ◽  
Vol 06 (02) ◽  
pp. 233-251 ◽  
Author(s):  
GREG HJORTH ◽  
SIMON THOMAS
Keyword(s):  
Abelian Groups ◽  
Classification Problem ◽  
Classification Problems ◽  
Borel Reducibility ◽  
Free Abelian Groups ◽  
Torsion Free

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

scholarly journals Kulikov's problem on universal torsion-free abelian groups revisited

2011 ◽  
Vol 43 (6) ◽  
pp. 1198-1204
Author(s):  
Saharon Shelah ◽  
Lutz Strüngmann
Keyword(s):  
Abelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

Near Isomorphism for a Class of Infinite Rank Torsion-Free Abelian Groups

2007 ◽  
Vol 35 (3) ◽  
pp. 1055-1072 ◽  
Author(s):  
Ekaterina Blagoveshchenskaya ◽  
Lutz Strüngmann
Keyword(s):  
Abelian Groups ◽  
Infinite Rank ◽  
Free Abelian Groups ◽  
Torsion Free
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