On complemented subgroups of finite groups

Long Miao

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 1019-1028
  • ISSN: 0011-4642

Abstract

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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 = H K and H ∩ 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.

How to cite

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Miao, Long. "On complemented subgroups of finite groups." Czechoslovak Mathematical Journal 56.3 (2006): 1019-1028. <http://eudml.org/doc/31088>.

@article{Miao2006,
abstract = {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.},
author = {Miao, Long},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite group; $p$-nilpotent group; primary subgroups; complemented subgroups; finite groups; -nilpotent groups; primary subgroups; complemented subgroups},
language = {eng},
number = {3},
pages = {1019-1028},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On complemented subgroups of finite groups},
url = {http://eudml.org/doc/31088},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Miao, Long
TI - On complemented subgroups of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 1019
EP - 1028
AB - 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.
LA - eng
KW - finite group; $p$-nilpotent group; primary subgroups; complemented subgroups; finite groups; -nilpotent groups; primary subgroups; complemented subgroups
UR - http://eudml.org/doc/31088
ER -

References

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  1. New criteria for the solvability of finite groups, J. Algebra 77 (1982), 234–246. (1982) MR0665175
  2. 10.1007/s000130050317, Arch. Math. 72 (1999), 161–166. (1999) MR1671273DOI10.1007/s000130050317
  3. 10.1112/blms/19.4.311, Bull. London Math. Soc. 19 (1987), 311–319. (1987) MR0887768DOI10.1112/blms/19.4.311
  4. The Theory of Classes of Groups, Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-London, 2000. (2000) Zbl1005.20016MR1862683
  5. The influence of minimal subgroups on the structure of finite groups, Southeast Asian Bulletin of Mathematics 22 (1998), 287–290. (1998) Zbl0937.20008MR1684151
  6. A characteristic property of soluble groups, J.  London Math. Soc. 12 (1937), 188–200. (1937) Zbl0016.39204MR1575073
  7. Endliche Gruppen  I, Springer-Verlag, Berlin-Heidelberg-New York, 1967. (1967) Zbl0217.07201MR0224703
  8. On Huppert’s characterization of finite supersoluble groups, In: Proc. Internat. Conf. Theory Groups, Canberra, 1965, , New York, 1967, pp. 209–215. (1967) Zbl0178.02101MR0217183
  9. 10.1007/BF01650529, Arch. Math. 12 (1961), 90–93. (1961) Zbl0099.01401MR0133365DOI10.1007/BF01650529
  10. A Course in the Theory of Groups, Springer-Verlag, Berlin-New York, 1993. (1993) MR1261639
  11. Finite groups with some subgroups of Sylow subgroups c-supplemented, J. Algebra 224 (2000), 467–478. (2000) Zbl0953.20010MR1739589
  12. An Introduction to Finite Groups, Science Press, Beijing, 1999. (Chinese) (1999) 
  13. The Structure of Finite Groups, Science Press, Beijing, 1982. (Chinese) (1982) 

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