| This thesis mainly investigates finite simple groups whose conjugacy class lengths satisfy some conditions.First,we prove that any finite simple group has two different conjugacy classes of same size.As a consequence,if each of conjugacy classes of a finite nonabelian group has different size,then the group is not simple.In addition,we also prove the following result:Let G be a finite nonabelian simple group.If the 2’-part of the greatest common divisor of any two of different conjugacy class lengths of G is square-free,then G is J1,2B2(q)with(q-1)(q2+1)being square-free,or G-A1(q)and one of the following holds:(1)q is an odd prime and((q-1)(q+1)2’is square-free.(2)q=2f≥4 and((q-1)(q+1》2’is square-free. |
