  We investigate topological AE(0) -groups class of which contains the class of
Polish groups as well as the class of all locally compact groups. We establish
the existence of an universal AE(0) -group of a given weight as well as the
existence of an universal action of AE(0) -group of a given weight on a AE(0)
-space of the same weight. A complete characterization of closed subgroups of
powers of the symmetric group is obtained. It is also shown that every AE
(0)-group is Baire isomorphic to the product of Polish groups. These results
are obtained by using the spectral descriptions of AE(0)-groups which are
presented in Section 3.
