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Sep 16, 2021 at 17:48 comment added YCor I think arbitrary compact $p$-adic Lie groups are Hopfian (as top. groups). A sufficient condition for a compact $p$-adic Lie group to be cohopfian is that the automorphism group of its Li algebra is volume preserving. This is indeed the case when the Lie algebra is semisimple (which is equivalent to your assumption).
Sep 12, 2021 at 9:54 history made wiki Post Made Community Wiki by Stefan Kohl
Mar 27, 2011 at 15:08 history answered Colin Reid CC BY-SA 2.5