Previous |  Up |  Next


Title: On complemented subgroups of finite groups (English)
Author: Miao, Long
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 56
Issue: 3
Year: 2006
Pages: 1019-1028
Summary lang: English
Category: math
Summary: A subgroup $H$ of a group $G$ is said to be complemented in $G$ if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K=1$. In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about $p$-nilpotent groups. (English)
Keyword: finite group
Keyword: $p$-nilpotent group
Keyword: primary subgroups
Keyword: complemented subgroups
MSC: 20D10
MSC: 20D15
MSC: 20D20
MSC: 20D40
idZBL: Zbl 1157.20323
idMR: MR2261674
Date available: 2009-09-24T11:40:54Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] Z. Arad, M. B. Ward: New criteria for the solvability of finite groups.J. Algebra 77 (1982), 234–246. MR 0665175
Reference: [2] A. Ballester-Bolinches, X. Guo: On complemented subgroups of finite groups.Arch. Math. 72 (1999), 161–166. MR 1671273, 10.1007/s000130050317
Reference: [3] F. Gross: Conjugacy of odd order Hall subgroup.Bull. London Math. Soc. 19 (1987), 311–319. MR 0887768, 10.1112/blms/19.4.311
Reference: [4] W. Guo: The Theory of Classes of Groups.Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-London, 2000. Zbl 1005.20016, MR 1862683
Reference: [5] W. Guo: The influence of minimal subgroups on the structure of finite groups.Southeast Asian Bulletin of Mathematics 22 (1998), 287–290. Zbl 0937.20008, MR 1684151
Reference: [6] P. Hall: A characteristic property of soluble groups.J.  London Math. Soc. 12 (1937), 188–200. Zbl 0016.39204, MR 1575073
Reference: [7] B. Huppert: Endliche Gruppen  I.Springer-Verlag, Berlin-Heidelberg-New York, 1967. Zbl 0217.07201, MR 0224703
Reference: [8] O. H. Kegel: On Huppert’s characterization of finite supersoluble groups.In: Proc. Internat. Conf. Theory Groups, Canberra, 1965, , New York, 1967, pp. 209–215. Zbl 0178.02101, MR 0217183
Reference: [9] O. H. Kegel: Produkte nilpotenter gruppen.Arch. Math. 12 (1961), 90–93. Zbl 0099.01401, MR 0133365, 10.1007/BF01650529
Reference: [10] D. J. Robinson: A Course in the Theory of Groups.Springer-Verlag, Berlin-New York, 1993. MR 1261639
Reference: [11] Y. Wang: Finite groups with some subgroups of Sylow subgroups c-supplemented.J. Algebra 224 (2000), 467–478. Zbl 0953.20010, MR 1739589
Reference: [12] M. Xu: An Introduction to Finite Groups.Science Press, Beijing, 1999. (Chinese)
Reference: [13] Y. Zhang: The Structure of Finite Groups.Science Press, Beijing, 1982. (Chinese)


Files Size Format View
CzechMathJ_56-2006-3_21.pdf 322.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo