| 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_2(2~3)or Ss(2~5)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_2(p~n)(n>1)and U_3(p~m)(m≥1).
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