**Papers Published**

- Stephen Ahearn, Mark L. Huber, Gary Sherman,
*Finite groups can be arbitrarily Hamiltonian*, Communications in Algebra, vol. 27 no. 3 (1999), pp. 1013--1016

(last updated on 2007/08/08)**Abstract:**

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.