a property of the haar measure of some special lca groups

the euclidean group (rn,+) where (n?n, plays a key role in harmonic analysis. if we consider the lebesgue measure ()nd?xr as the haar measure of this group then 12(2)()nd?x=d?rr. 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 k?, there exists a constant such that 0kc>()(2)kkk?a=c?a for every measurable subset a of k. moreover we will characterize this constant for some special groups.