Let G = {(x; y) : x in R; y > 0}. With (x; y)(u; v) = (x + yu; yv), G
is a group .If topologize G as a subset of R^2, it is known that G is a locally compact
group that is not unimodular.(see (15.17) of Hewitt-Ross) Is there another
topological structure of the group G such that G be a locally compact group and also subgroup K = {(0; y) : y > 0} be compact?