Math @ Duke
Publications [#10391] of Mark Huber
- Stephen Ahearn, Mark L. Huber, Gary Sherman, Finite groups can be arbitrarily Hamiltonian,
Communications in Algebra, vol. 27 no. 3
(last updated on 2007/08/08)
In finite groups that are not abelian, at most 3/4 of
pairs of elements will commute. A natural question is
whether this gap extends to measures of "Hamiltonianess".
In fact, this paper shows that for any rational number r
between 0 and 1, there exist groups where the probability
that a subgroup chosen uniformly at random from the set of
subgroups is normal is exactly r. The proof technique was
suggested through computer experimentation.
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