let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .

‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in w...

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

A locally compact topological group G is called an (H) group if G has a maximal compact normal subgroup with Lie factor. In this note, we study the problem when a locally compact group is an (H) group. Let G be a locally compact Hausdorff topological group. Let G0 be the identity component of G. If G/G0 is compact, then we say that G is almost connected. The structure of almost connected locall...