摘要
This paper studies the relations between T.I.conditions and cyclic conditions on theSylow p-subgroups of a finite group G.As examples,the following two results are proved.1.Let G be a finite group with a T.I.Sylow p-subgroup P.If p=3 or 5,wesuppose G contains no composition factors isomorphic to the simple group L<sub>2</sub>（2<sup>3</sup>）or Ss（2<sup>5</sup>）respectively.If G has a normal subgroup W such that p|（|W|,|G/W|）,then G isp-solvable.2.Let G be a finite group with a T.I.Sylow p-subgroup P.Suppose p】11 and P isnot normal in G.Then P is cyclic if and only if G has no composition factors L<sub>2</sub>（p<sup>n</sup>）（n】1）and U<sub>3</sub>（p<sup>m</sup>）（m≥1）.
This paper studies the relations between T.I.conditions and cyclic conditions on the Sylow p-subgroups of a finite group G.As examples,the following two results are proved. 1.Let G be a finite group with a T.I.Sylow p-subgroup P.If p=3 or 5,we suppose G contains no composition factors isomorphic to the simple group L_2(2~3)or Ss(2~5) respectively.If G has a normal subgroup W such that p|(|W|,|G/W|),then G is p-solvable. 2.Let G be a finite group with a T.I.Sylow p-subgroup P.Suppose p>11 and P is not normal in G.Then P is cyclic if and only if G has no composition factors L_2(p^n)(n >1)and U_3(p^m)(m≥1).
