# Centralizers in Hall’s universal groups and direct limits of finitary symmetric groups

2014-01-01
kegel, Otto
Kuzucuoğlu, Mahmut
We study the centralizers of finite subgroups in Hall's universal group. We describe the structure of the centralizers of arbitrary finite subgroups in the groups S(\xi) and FSym(\kappa)(\xi) where S(\xi)'s are obtained as direct limits of finite symmetric groups and FSym(\kappa)(\xi)'s are obtained as direct limits of finitary symmetric groups on the set of infinite cardinality \kappa.