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Let      G G       be a locally compact group and      H H       a closed subgroup of      G G       such that the homogeneous space      G / H G/H       admits a finite invariant measure. Let      Z G ( H ) {Z_G}(H)       be the centralizer of      H H       in      G G      . It is shown that if      G G       is connected then      Z G ( H ) {Z_G}(H)       modulo its center is compact. If      G G       is only assumed to be locally connected it is shown that the commutator subgroup of      Z G ( H ) {Z_G}(H)       has compact closure. Consequences of these results are found for special classes of groups, such as Lie groups. An example of a totally disconnected group      G G       is given to show that the results for      Z G ( H ) {Z_G}(H)       need not hold if      G G       is not connected or locally connected.

On centralizers of generalized uniform subgroups of locally compact groups