Of course the probability will depend on the measure put on the groups, and it is trivial to define many such measures if they do not have to be useful or significant in any way! But is there such a measure that is actually useful? Or are there several useful ones?
2026-03-26 13:30:14.1774531814
Is there a meaningful measure of the probability for a finite group to be commutative?
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The answer to the posted question is no: there is no useful notion of probability over all finite groups for measuring the commutative groups.
Maybe if I were more used to finite structures I would have asked about probability for any finite order $n$ in the first place, rather than for all finite groups.
But certainly, for this question of commutative groups, the asymptotics in the order $n$ show the proportion of Abelian groups is vanishingly small. So there is no interest in assigning a probability measure on all finite groups for this purpose.