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Strong duality for metacyclic groups

Part of: Algebraic structures Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

R. Quackenbush  and
C. S. Szabó
R. Quackenbush
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada e-mail: qbush@cc.umanitoba.ca
C. S. Szabó
Affiliation:
Department of Algebra and Number Theory, ELTE, Budapest, Hungary e-mail: csaba@cs.elte.hu
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Abstract

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Davey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

Keywords

metacyclic groupduality

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 08A05: Structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 3 , December 2002 , pp. 377 - 392
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Clark, D. M. and Davey, B. A., Natural dualities for the working algebraist (CUP, Cambridge, 1998).Google Scholar
[2]Davey, B. A. and Quackenbush, R. W., ‘Natural duality for dihedral groups’, J. Ausiral. Math. Soc. (Ser. A) 61 (1996), 216–228.Google Scholar
[3]Olshanskii, A. Ju., ‘Varieties of finitely approximable groups’, Math. USSR—Izvestia 3 (1969), 867–877.CrossRefGoogle Scholar
[4]Quackenbush, R. and Szabó, Cs., ‘Nilpotent groups are not dualizable’, J. Aust. Math. Soc. 72 (2001), 173–179.CrossRefGoogle Scholar
[5]Robinson, D. J. S., A course in the theory of groups (Springer, New York, 1982).CrossRefGoogle Scholar