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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  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
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  12. An Introduction to Finite Groups, Science Press, Beijing, 1999. (Chinese) (1999) 
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