Compactly Covered Subgroup of Locally Compact Group
by
Yu.N. Mukhin
Institute of Mathematics and Mechanics, Ekaterinburg

A subgroup H of a locally compact group G is called compactly covered if it is union of compact subgroups. The following questions are natural.

A. Whether the union \Phi(G) of all compact subgroup of G is 0-dimensional?

B. Whether a maximal compactly covered subgroup of G is closed if G is 0-dimensional?

C .Will the closure of a compactly covered normal subgroup of G be compactly covered?

D . If N is a closed normal subgroup od G with N and G/N being compactly covered, will G be compactly covered?

E . Is exists in G the greatest compactly covered normal subgroup P(G)? If yes, will P(G) be closed?

We gave (1981) positive answers on A - E under some additional condition on G. Willis (1995) positively answered the question A, the result solves B affirmatively. Now we succeed to get affirmative amswers on C, D, E.

It is proved that P(G) = { x in G | x\Psi(G) subset \Psi(G) } and a characteristic of P(G) is given in terms of the lattice of all closed subgroups of G.

Date received: June 24, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caai-80.