【摘要】 群G的一个子群H称为半置换的,若对G的任意子群K,只要(|H|,|K|)=1,就有HK=KH;H称为s-半置换的,若对G的任意Sylow p-子群P,只要(p,|H|)=1,就有HP=PH.本文研究极大子群和极小子群的某些子群的s-半置换性对群构造的影响,推广和改进了Asaad及王品超等人所得的结果.更多还原

【Abstract】 A subgroup H of a group G is said to be semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, we extend and improve some of Asaad and Pingchao Wang’s results by examining the influence of s-semipermutability on the structure of groups.更多还原