ON THE FINITE GROUP WITH A.T.I SYLOW P-SUBGROUP |
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Authors: | Zhang Jiping |
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Institution: | Department of Mathematics, Beijing Univercity, Beijing, China. |
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Abstract: | 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 S(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>ll 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_{s}(p^{m})(m\geq 1). |
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Keywords: | |
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