scholarly journals Countably compact topological group topologies on free Abelian groups from selective ultrafilters

2007 ◽  
Vol 154 (7) ◽  
pp. 1470-1480 ◽  
Author(s):  
Roberto E. Madariaga-Garcia ◽  
Artur Hideyuki Tomita
Keyword(s):  
Topological Group ◽  
Abelian Groups ◽  
Compact Topological Group ◽  
Countably Compact ◽  
Free Abelian Groups

scholarly journals A countably compact topological group with the non-countably pracompact square

2020 ◽  
Vol 279 ◽  
pp. 107251
Author(s):  
Serhii Bardyla ◽  
Alex Ravsky ◽  
Lyubomyr Zdomskyy
Keyword(s):  
Topological Group ◽  
Compact Topological Group ◽  
Countably Compact

Successors of locally compact topological group topologies on abelian groups

2020 ◽  
Vol 249 (1) ◽  
pp. 71-93 ◽  
Author(s):  
Dekui Peng ◽  
Wei He ◽  
Mikhail Tkachenko ◽  
Zhiqiang Xiao
Keyword(s):  
Topological Group ◽  
Abelian Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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.

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