| 关于正规P—补 |
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| 引用本文： | 邓辉文.关于正规P—补[J].西南师范大学学报(自然科学版),1990,15(2):170-173. |
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| 作者姓名： | 邓辉文 |
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| 作者单位： | 西南师范大学计算机科学系 |
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| 摘 要： | 本短文得到的主要结果为:(1)设G为p-可解群,P∈Syl_p G,P循环,则G有正规p-补或GL有正规p-补.(2)设p为|G|的最小素因子,P∈Syl_pG,P正则或为Hamilton 2-群,则G有正规p-补的充要条件是对任意P的含Φ(P)且阶为p|φ(P)|的子群均在N_G(P)中类正规.
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| 关 键 词： | 有限群 正规P－补 P循环 类正规 |
ON NORMAL p-COMPLEMENTS |
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| Deng Huiwen.ON NORMAL p-COMPLEMENTS[J].Journal of Southwest China Normal University(Natural Science),1990,15(2):170-173. |
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| Authors: | Deng Huiwen |
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| Institution: | Southwest China Teachers University |
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| Abstract: | Let G be a finite group and P a Sylow p-subgroup of G.Theorem A If G is p-solvable and P is cyclic, then either G or G' has a normal p-complement.Theorem B Suppose that p is the smallest prime divisor of |G| and P is either regular or a Hamiltonian 2-group. Then G has a normal p-complement if, and only if. every subgroup of P which contains (P) and is of order is pronorma.l in NG(P). |
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| Keywords: | pronormal normal p-complements cyclic Sylow p-subgroups |
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