Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T21:09:20.159Z Has data issue: false hasContentIssue false
  • English
  • Français

FINITE GROUPS WITH COMPLEMENTED 2-MINIMAL $p$-SUBGROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  11 March 2020

YU ZENG Open the ORCID record for YU ZENG [Opens in a new window]
YU ZENG*
Affiliation:
Department of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, China email [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

For a given prime $p$, we investigate the finite groups all of whose 2-minimal $p$-subgroups are complemented.

Keywords

finite groupcomplemented subgroup

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 430 - 438
Check for updates
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Project supported by the NSF of China (no. 11671324).

References

Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., ATLAS of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups (Oxford University Press, Oxford, 1985).Google Scholar
Gorchakov, Y. M., ‘Primitively factorizable groups’, Dokl. Akad. Nauk 131(6) (1960), 1246–1248; (in Russian).Google Scholar
Guralnick, R. M., ‘Subgroups of prime power index in a simple group’, J. Algebra 81(2) (1983), 304–311.CrossRefGoogle Scholar
Hall, P., ‘Complemented groups’, J. Lond. Math. Soc. (2) 12(3) (1937), 201–204.10.1112/jlms/s1-12.2.201CrossRefGoogle Scholar
Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).10.1007/978-3-642-64981-3CrossRefGoogle Scholar
Monakhov, V. S. and Kniahina, V. N., ‘Finite groups with complemented subgroups of prime orders’, J. Group Theory 18(6) (2015), 905–912.Google Scholar
Qian, G., ‘Nonsolvable groups with few primitive character degrees’, J. Group Theory 21(2) (2018), 295–318.10.1515/jgth-2017-0037CrossRefGoogle Scholar
Qian, G. and Shi, W., ‘The largest character degree and the Sylow subgroups of finite groups’, J. Algebra 277 (2004), 165–171.10.1016/j.jalgebra.2003.02.009CrossRefGoogle Scholar
Qian, G. and Tang, F., ‘Finite groups with certain subgroups of prime power order complemented’, J. Algebra 423 (2015), 950–962.10.1016/j.jalgebra.2014.11.001CrossRefGoogle Scholar
Qian, G. and Zeng, Y., ‘On partial cap-subgroups of finite groups’, J. Algebra 546 (2020), 553–565.10.1016/j.jalgebra.2019.11.007CrossRefGoogle Scholar
Zeng, Y., ‘Finite groups with complemented minimal p-subgroups’, Comm. Algebra, 48(2) (2020), 644–650.10.1080/00927872.2019.1654492CrossRefGoogle Scholar