Finite Simple Groups The 2- Or 2'-Parts Of Whose Irreducible Character Degrees Satisfy Some Conditions

This thesis investigates finite simple groups with the 2-or 2'-parts of degrees of irre-ducible characters satisfying some conditions.Specifically,it mainly proves the following results:1.Let G be a finite nonabelian simple group.If all degrees of irreducible charac-ters of G are not divisible by 8,then G=A7 or A1(q)and q?±3(mod 8).2.Let G be a finite nonabelian simple group.If any of the odd degrees of irreducible characters of G is not a prime,then G=A1(q),where q? 5 is an prime and q+(-1)(q-1)/2)/2 is a prime.