Abstract
A subgroup $H$ of a finite group $G$ is said to be ``semi-cover-avoiding in $G$'', if there exists a chief series of $G$ such that $H$ covers or avoids every chief factor of the chief series. In this article, we will consider some 2-maximal subgroups with the property of semi-cover-avoiding of a group $G$ and explore the structure of $G$.
Keywords
semi-cover-avoiding proterty soluble groups maximal subgroups 2-maximal subgroups Sylow p-subgroups p-solvable
Supporting Institution
NSFC；NSFC；NSFC-RFBR； the Natural Science Foundation of Jiangsu Province
Project Number
Grant \# 11871062；Grant\ # 11701223；Grant\ # 12011530061；Grant\ # BK20181451
References
- [1] M. Bianchi, A. G. B. Mauri and P. Hauck, On finite groups with nilpotent Sylownormalizers, Arch. Math. 47 (3), 193-197, 1986.
- [2] K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992.
- [3] Y. Fan, X. Guo and K. P. Shum, Remarks on two generalizations of normality of subgroups, Chinese J. Contemp. Math. 27 (2), 139-146, 2006.
- [4] W. Guo, The Theory of Classes of Groups, Science Press-Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-london, 2000.
- [5] X. Guo and K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Appl. Algebra 181 (2-3), 297-308, 2003.
- [6] X. Guo, J. Wang and K. P. Shum, On semi-cover-avoiding maximal subgroups and solvability of finite groups, Comm. Algebra, 34 (9), 3235-3244, 2006.
- [7] B. Huppert, Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60, 409-434, 1954.
- [8] M. N. Konovalova, V. S. Monakhov and I. L. Sokhor, On 2-maximal subgroups of finite groups, Comm. Algebra, 50 (1), 96-103, 2022.
- [9] S. Li, H. Liu and D. Liu, The solvability between finite groups and semi-subnormalcover- avoidance subgroups, J. Math. 37 (6), 1303-1308, 2017.
- [10] L. Miao and J. Zhang, On a class of non-solvable groups, J. Algebra, 496, 1-10, 2018.
- [11] Y. Wang, L. Miao, Z. Gao and W. Liu, The influence of second maximal subgroups on the generalized p-solvability of finite groups, Comm. Algebra, 50 (6), 2584-2591, 2022.
Abstract
Project Number
Grant \# 11871062；Grant\ # 11701223；Grant\ # 12011530061；Grant\ # BK20181451
References
- [1] M. Bianchi, A. G. B. Mauri and P. Hauck, On finite groups with nilpotent Sylownormalizers, Arch. Math. 47 (3), 193-197, 1986.
- [2] K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992.
- [3] Y. Fan, X. Guo and K. P. Shum, Remarks on two generalizations of normality of subgroups, Chinese J. Contemp. Math. 27 (2), 139-146, 2006.
- [4] W. Guo, The Theory of Classes of Groups, Science Press-Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-london, 2000.
- [5] X. Guo and K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Appl. Algebra 181 (2-3), 297-308, 2003.
- [6] X. Guo, J. Wang and K. P. Shum, On semi-cover-avoiding maximal subgroups and solvability of finite groups, Comm. Algebra, 34 (9), 3235-3244, 2006.
- [7] B. Huppert, Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60, 409-434, 1954.
- [8] M. N. Konovalova, V. S. Monakhov and I. L. Sokhor, On 2-maximal subgroups of finite groups, Comm. Algebra, 50 (1), 96-103, 2022.
- [9] S. Li, H. Liu and D. Liu, The solvability between finite groups and semi-subnormalcover- avoidance subgroups, J. Math. 37 (6), 1303-1308, 2017.
- [10] L. Miao and J. Zhang, On a class of non-solvable groups, J. Algebra, 496, 1-10, 2018.
- [11] Y. Wang, L. Miao, Z. Gao and W. Liu, The influence of second maximal subgroups on the generalized p-solvability of finite groups, Comm. Algebra, 50 (6), 2584-2591, 2022.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Project Number | Grant \# 11871062；Grant\ # 11701223；Grant\ # 12011530061；Grant\ # BK20181451 |
| Early Pub Date | August 15, 2023 |
| Publication Date | April 23, 2024 |
| Published in Issue | Year 2024 |