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INFLUENCE OF STRONGLY CLOSED 2-SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS

Published online by Cambridge University Press:  10 March 2011

HUNG P. TONG-VIET
HUNG P. TONG-VIET*
Affiliation:
Department of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK e-mail: tongviet@maths.bham.ac.uk
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Abstract

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Let H ≤ K be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever ag ∈ K, where a ∈ H, g ∈ G, then ag ∈ H. In this paper, we investigate the structure of a group G under the assumption that every subgroup of order 2m (and 4 if m = 1) of a 2-Sylow subgroup S of G is strongly closed in S with respect to G. Some results related to 2-nilpotence and supersolvability of a group G are obtained. This is a complement to Guo and Wei (J. Group Theory13(2) (2010), 267–276).

Keywords

Primary 20D20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 577 - 581
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Asaad, M., On p-nilpotence and supersolvability of finite groups, Commun. Algebra 34 (1) (2006), 189–195.CrossRefGoogle Scholar
2.Baumann, B., Endliche nichtauflösbare Gruppen mit einer nilpotenten maximalen Untergruppe, J. Algebra 38 (1) (1976), 119–135.CrossRefGoogle Scholar
3.Bianchi, M., Mauri, A., Herzog, M. and Verardi, L., On finite solvable groups in which normality is a transitive relation, J. Group Theory 3 (2) (2000), 147–156.CrossRefGoogle Scholar
4.Goldschmidt, D., 2-fusion in finite groups, Ann. Math. 99 (3) (1974), 70–117.CrossRefGoogle Scholar
5.Goldschmidt, D., Strongly closed 2-subgroups of finite groups, Ann. Math. 102 (3) (1975), 475–489.CrossRefGoogle Scholar
6.Gorenstein, D., Finite groups, 2nd edn. (Chelsea Publishing Company, New York, 1980).Google Scholar
7.Guo, X. and Wei, X., The influence of -subgroups on the structure of finite groups, J. Group Theory 13 (2) (2010), 267–276.CrossRefGoogle Scholar
8.Huppert, B., Endliche Gruppen I, in Die Grundlehren der Mathematischen Wissenschaften, band vol. 134 (Springer-Verlag, Berlin-New York, 1967).Google Scholar
9.Isaacs, M., Finite group theory, in Graduate Studies in Mathematics, vol. 92 (AMS, Providence, RI, 2008).Google Scholar