The author considers the classes of conjugate elements in topological
Definition. A topological group is called an FC-group, if the closure
of every class of conjugate elements is compact, and one locally normal
if everyone of its elements is contained in a compact invariant subgroup.
Each locally normal group G is obviously a periodic * FC-group. The
converse assertion is proved in this paper for groups with an open compact
The main result is the following.
Theorem. Let G be an FC-group with an open compact subgroup.
Then the set of all compact elements of G generates an open invariant
subgroup P(G); the factor-group G/P(G) is a discrete torsion-free Abe-
Citation Example:Ushakov V. I. Classes of conjugate elements in topological groups // Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 366-371.