| Title:
|
On TI-subgroups and QTI-subgroups of finite groups (English) |
| Author:
|
Chen, Ruifang |
| Author:
|
Zhao, Xianhe |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
179-185 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a group. A subgroup $H$ of $G$ is called a TI-subgroup if $H\cap H^g=1$ or $H$ for every $g\in G$ and $H$ is called a QTI-subgroup if $C_G(x) \le N_G(H)$ for any $1\neq x\in H$. In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized. (English) |
| Keyword:
|
TI-subgroup |
| Keyword:
|
QTI-subgroup |
| Keyword:
|
maximal subgroup |
| Keyword:
|
Frobenius group |
| Keyword:
|
solvable group |
| MSC:
|
20D10 |
| idZBL:
|
07217127 |
| idMR:
|
MR4078352 |
| DOI:
|
10.21136/CMJ.2019.0203-18 |
| . |
| Date available:
|
2020-03-10T10:16:56Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148048 |
| . |
| Reference:
|
[1] Arad, Z., Herfort, W.: Classification of finite groups with a CC-subgroup.Commun. Algebra 32 (2004), 2087-2098. Zbl 1070.20023, MR 2099578, 10.1081/AGB-120037209 |
| Reference:
|
[2] Gorenstein, D.: Finite Groups.Harper's Series in Modern Mathematics, Harper & Row, New York (1968). Zbl 0185.05701, MR 0231903 |
| Reference:
|
[3] Guo, X., Li, S., Flavell, P.: Finite groups whose abelian subgroups are TI-subgroups.J. Algebra 307 (2007), 565-569. Zbl 1116.20014, MR 2275363, 10.1016/j.jalgebra.2006.10.001 |
| Reference:
|
[4] Huppert, B.: Endliche Gruppen I.Die Grundlehren der Mathematischen Wissenschaften 134, Springer, Berlin German (1967). Zbl 0217.07201, MR 0224703, 10.1007/978-3-642-64981-3 |
| Reference:
|
[5] Kurzweil, H., Stellmacher, B.: The Theory of Finite Groups. An Introduction.Universitext, Springer, New York (2004). Zbl 1047.20011, MR 2014408, 10.1007/b97433 |
| Reference:
|
[6] Li, S.: Finite non-nilpotent groups all of whose second maximal subgroups are TI-groups.Math. Proc. R. Ir. Acad. 100A (2000), 65-71. Zbl 0978.20012, MR 1882200 |
| Reference:
|
[7] Lu, J., Guo, X.: Finite groups all of whose second maximal subgroups are QTI-subgroups.Commun. Algebra 40 (2012), 3726-3732. Zbl 1259.20021, MR 2982892, 10.1080/00927872.2011.594135 |
| Reference:
|
[8] Lu, J., Pang, L.: A note on TI-subgroups of finite groups.Proc. Indian Acad. Sci., Math. Sci. 122 (2012), 75-77. Zbl 1272.20018, MR 2909585, 10.1007/s12044-012-0055-x |
| Reference:
|
[9] Lu, J., Pang, L., Zhong, X.: Finite groups with non-nilpotent maximal subgroups.Monatsh. Math. 171 (2013), 425-431. Zbl 1277.20017, MR 3090801, 10.1007/s00605-012-0432-7 |
| Reference:
|
[10] Qian, G., Tang, F.: Finite groups all of whose abelian subgroups are QTI-subgroups.J. Algebra 320 (2008), 3605-3611. Zbl 1178.20014, MR 2455518, 10.1016/j.jalgebra.2008.08.009 |
| Reference:
|
[11] Robinson, D. J. S.: A Course in the Theory of Groups.Graduate Texts in Mathematics 80, Springer, New York (1996). Zbl 0836.20001, MR 1357169, 10.1007/978-1-4419-8594-1 |
| Reference:
|
[12] Shi, J., Zhang, C.: Finite groups in which all nonabelian subgroups are TI-subgroups.J. Algebra Appl. 13 (2014), Article ID 1350074, 3 pages. Zbl 1285.20020, MR 3096855, 10.1142/S0219498813500746 |
| Reference:
|
[13] Walls, G.: Trivial intersection groups.Arch. Math. 32 (1979), 1-4. Zbl 0388.20011, MR 0532840, 10.1007/BF01238459 |
| . |
