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GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 February 2012

J. C. BEIDLEMAN  and
H. HEINEKEN
J. C. BEIDLEMAN*
Affiliation:
Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, USA (email: clark@ms.uky.edu)
H. HEINEKEN
Affiliation:
Institut für Mathematik, Universität Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany (email: heineken@mathematik.uni-wuerzburg.de)
*
✉For correspondence; e-mail: clark@ms.uky.edu
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Abstract

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We consider the class of solvable groups in which all subnormal subgroups have subnormal normalizers, a class containing many well-known classes of solvable groups. Groups of this class have Fitting length three at most; some other information connected with the Fitting series is given.

Keywords

subnormal subgroupspermutable subgroupshypercentrally embedded subgroups

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 11 - 21
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Agrawal, R. K., ‘Finite groups where subnormal subgroups permute with all Sylow subgroups’, Proc. Amer. Math. Soc. 47 (1975), 77–83.CrossRefGoogle Scholar
[2]Asaad, M., Ballester-Bolinches, A. and Esteban-Romero, R., Products of Finite Groups, Expositions in Mathematics, 53 (W. de Gruyter, Berlin–New York, 2010).Google Scholar
[3]Huppert, B., Endliche Gruppen I (Springer, Berlin–Heidelberg–New York, 1967).CrossRefGoogle Scholar
[4]Kegel, O. H., ‘Sylow-Gruppen und Subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205–221.CrossRefGoogle Scholar
[5]Maier, R. and Schmid, P., ‘The embedding of quasinormal subgroups in finite groups’, Math. Z. 131 (1973), 269–272.CrossRefGoogle Scholar
[6]Robinson, D. J. S., A course in the Theory of Groups, 2 edn, Graduate Texts in Mathematics, 80 (Springer, Berlin–Heidelberg–New York, 1996).CrossRefGoogle Scholar
[7]Schmid, P., ‘Subgroups permutable with all Sylow subgroups’, J. Algebra 207 (1998), 285–293.CrossRefGoogle Scholar