A Property of the Haar Measure of Some Special Lca Groups.

The euclidean group (rn,+) where (n(element of)n), plays a key role in harmonic analysis. if we consider the lebesgue measure d(mu)rn(x) as the haar measure of this group then 1/2d(mu) rn(2x)=d(mu)rn(x). in this article we look for lca groups k, whose haar measures have a similar property. in fact we will show that for some lca groups k with the haar measure (mu)k, there exists a constant ck>0 such that (mu)k(a)= ck(mu)k (a^2) for every measurable subset a of k. moreover we will characterize this constant for some special groups.