Math Graduate Student Seminar

Probability threshold for group isomorphism

Edward Hou, Mathematics Department, Caltech,

In 1968 Erdős and Turán proved essentially that a (finite) group is commutative as long as more than 5/8 of the pairs in the group commute. We discuss a similar threshold result: Two groups are isomorphic as long as there is a bijection which preserves more than 7/9 of group multiplication.

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