scholarly journals Effectively closed subgroups of the infinite symmetric group

2018 ◽  
Vol 146 (12) ◽  
pp. 5421-5435
Author(s):  
Noam Greenberg ◽  
Alexander Melnikov ◽  
Andre Nies ◽  
Daniel Turetsky

Author(s):  
Alexei Borodin ◽  
Grigori Olshanski


1987 ◽  
Vol 106 ◽  
pp. 143-162 ◽  
Author(s):  
Nobuaki Obata

The infinite symmetric group is the discrete group of all finite permutations of the set X of all natural numbers. Among discrete groups, it has distinctive features from the viewpoint of representation theory and harmonic analysis. First, it is one of the most typical ICC-groups as well as free groups and known to be a group of non-type I. Secondly, it is a locally finite group, namely, the inductive limit of usual symmetric groups . Furthermore it is contained in infinite dimensional classical groups GL(ξ), O(ξ) and U(ξ) and their representation theories are related each other.



2012 ◽  
Vol 273 (1-2) ◽  
pp. 303-310 ◽  
Author(s):  
Mohamed Bouali






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