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The Influence of s-quasinormally Embedded and Weakly s-supplemented Subgroups on the Structure of Finite Groups

Author: LinDan
Tutor: LiXianHua
School: Suzhou University
Course: Basic mathematics
Keywords: s- quasinormal embedded XΦ- super- center Weak s- can complement p - nilpotent groups
CLC: O152.1
Type: Master's thesis
Year: 2011
Downloads: 12
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Abstract


The proposed regular embedding and weak s- complement with a finite group structure between this study subgroup s- main results and prove in the second and third chapters . ( 1 ) in the second chapter , we get the following theorem . Theorem Let E ( ? ) G , p is divisible | E | a prime factor , P E a Sylow p- subgroup if there subgroup D of P , so lt ; | D | lt; P |, and P any | D | bands and 4 cyclic subgroup in G or p- nilpotent complement , or s- contemplated formal embedded : (Ⅰ) if p | G | smallest prime factor , E / OP ' ( E ) ≤ ZuΦ ( G / Op ' ( E )) (II ) If p is the smallest prime factor of | E | , E / Op '( E ) ≤ ZuΦ ( G / Op '(E)). Theorem Let E ( ? ) G | P | is non- circulating E Sylow p- subgroup P subgroup D such that 1 lt ; | D | the lt ; | P | . If any of P | D | order subgroup 4 cyclic subgroup in G s- quasinormal embedding , E ≤ ZUΦ ( G ) ( 2 ) in the third chapter , the use of maximal subgroups of the Sylow subgroup sufficient condition for finite group p - nilpotency group weak s- complementary , which generalize some known results ;

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Finite group theory
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