2018
Том 70
№ 4

Всі номери

Ушаков В. І.

Публікацій: 1
Стаття (російською)

Классы сопряженных элементов в топологических группах

Ушаков В. И.

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Укр. мат. журн. - 1962. - 14, № 4. - С. 366-371

The author considers the classes of conjugate elements in topological groups. 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 subgroup. 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- Han group.