On some infinite dimensional linear groups

Abstract

Let F be a field and A an (infinite dimensional) vector space over F. A group G of linear transormations of A is said to be finitary linear if for each element g 2 G the centralizer CA(g) has finite codimension over F. Finitary linear groups are natural analogs of FC-groups (i.e. groups with finite conjugacy classes). In this paper we consider linear analogs of groups with boundedly finite conjugacy classes, and also some generalizations corresponding to groups with Chernikov conjugacy classes