Browse > Article
http://dx.doi.org/10.4134/CKMS.2013.28.1.055

A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS  

He, Xuanli (Department of Mathematics Guangxi University)
Qiao, Shouhong (School of Applied Mathematics Guangdong University of Technology)
Wang, Yanming (Lingnan College and Department of Mathematics Sun Yat-sen University)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.1, 2013 , pp. 55-62 More about this Journal
Abstract
In [5], Johnson introduced the primitivity of subgroups and proved that a finite group G is supersolvable if every primitive subgroup of G has a prime power index in G. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize T-group and the solvable $PST_0$-groups.
Keywords
finite groups; primitive subgroups; maximal subgroups; the solvable $PST_0$-groups;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. K. Agrawal, Finite groups whose subnormal subgroups permute with all Sylow subgroups, Proc. Amer. Math. Soc. 47 (1975), 77-83.   DOI   ScienceOn
2 K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter & Co., Berlin, 1992.
3 W. Guo, K. P. Shum, and A. Skiba, On primitive subgroups of finite groups, Indian J. Pure Appl. Math. 37 (2006), no. 6, 369-376.
4 B. Huppert, Endliche Gruppen. I, Springer-Verlag, 1967.
5 D. L. Johnson, A note on supersoluble groups, Canad. J. Math. 23 (1971), 562-564.   DOI
6 D. J. S. Robinson, A note on finite groups in which normality is transitive, Proc. Amer. Math. Soc. 19 (1968), 933-937.   DOI   ScienceOn
7 D. J. S. Robinson, A Course in the Theory of Groups, 2nd ed., Springer-Verlag, New York, 1996.