G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.© BrainMass Inc. brainmass.com June 22, 2018, 7:26 am ad1c9bdddf
This is a proof regarding conjugacy classes and a non-identity element.