ON SUBGROUPS RELATED TO THE TENSOR CENTER

The tensor center of a group G is the set of elements a in G such that a(sleet) g = 1_(sleet) for all g in G. It is a characteristic subgroup of G contained in its center. We introduce tensor analogues of various other subgroups of a group such as centralizers and 2-Engel elements and investigate their embedding in the group as well as interrelationships between those subgroups.