Finite Groups Whose n-Maximal Subgroups Are Modular

Сибирский математический журнал

J. Huang¹ 

[1] School of Mathematics and Statistics Jiangsu Normal University

关键词: finite group;    modular subgroup;    n-maximal subgroup;    nearly nilpotent group;    strongly supersoluble group;   

DOI  :  10.1134/S0037446618030187

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let G be a finite group. If Mn< Mn−1< · · · < M1< M0 = G with Mi a maximal subgroup of Mi−1 for all i = 1,..., n, then Mn (n > 0) is an n-maximal subgroup of G. A subgroup M of G is called modular provided that (i) 〈X,M ∩ Z〉 = 〈X,M〉 ∩ Z for all X ≤ G and Z ≤ G such that X ≤ Z, and (ii) 〈M,Y ∩ Z〉 = 〈M,Y 〉 ∩ Z for all Y ≤ G and Z ≤ G such that M ≤ Z. In this paper, we study finite groups whose n-maximal subgroups are modular.

【 授权许可】

CC BY