Finite Groups Whose n-Maximal Subgroups Are Modular
- Authors: Huang J.1, Hu B.1, Zheng X.1
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Affiliations:
- School of Mathematics and Statistics Jiangsu Normal University
- Issue: Vol 59, No 3 (2018)
- Pages: 556-564
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171930
- DOI: https://doi.org/10.1134/S0037446618030187
- ID: 171930
Cite item
Abstract
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.
About the authors
J. Huang
School of Mathematics and Statistics Jiangsu Normal University
Email: hubin118@126.com
China, Xuzhou
B. Hu
School of Mathematics and Statistics Jiangsu Normal University
Author for correspondence.
Email: hubin118@126.com
China, Xuzhou
X. Zheng
School of Mathematics and Statistics Jiangsu Normal University
Email: hubin118@126.com
China, Xuzhou