Topological quasi-Hamiltonian groups.

*(Russian)*Zbl 0713.22004A locally compact group G is called a topological quasi-Hamiltonian group (tqH-group) if for any closed subgroups X and Y the closures of XY and of YX coincide. Abelian groups and topological Hamiltonian groups are tqH- groups. If a tqH-group is discrete then it is quasi-Hamiltonian. Such groups were studied by K. Iwasawa and G. Zappa [see the book: M. Suzuki, Structure of a group and the structure of its lattice of subgroups (1956; Zbl 0070.254)]. The purpose of the paper reviewed is to get a description of tqH-groups. Let us show one of the results. A compact covered group G is called D-group (here the author writes the Cyrillic letter D) if for any cycle in the lattice L(G) the modular identity is true. Then for a group G containing pure elements the following statements are equivalent: G is tqH-group, G is D-group.

Reviewer: V.F.Molchanov

##### MSC:

22D05 | General properties and structure of locally compact groups |

22A05 | Structure of general topological groups |

20E15 | Chains and lattices of subgroups, subnormal subgroups |