The number of κ — Free abelian groups and the size of Ext

1977 ◽  
pp. 323-331 ◽  
Author(s):  
Alan Mekler
Keyword(s):  
Abelian Groups ◽  
Free Abelian Groups

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

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.

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.

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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