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Jun 10, 2012 at 21:39 vote accept Dave Penneys
Apr 11, 2012 at 7:52 comment added Colin Reid I think 1. and 3. are already incompatible by your argument. Also, just an aside: If $G$ is a totally disconnected, locally compact group and $H$ is an open compact subgroup, then the homomorphism you define is the modular function of the group: it measures the extent to which a right translation rescales a left Haar measure.
Apr 10, 2012 at 21:55 history edited Dave Penneys CC BY-SA 3.0
edited body; edited body
Apr 10, 2012 at 19:06 history edited Dave Penneys CC BY-SA 3.0
some typos fixed
Apr 10, 2012 at 17:07 history answered Dave Penneys CC BY-SA 3.0