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Natural dualities for dihedral varieties

Part of: Algebraic structures Varieties

Published online by Cambridge University Press:  09 April 2009

B. A. Davey  and
R. W. Quackenbush
B. A. Davey
Affiliation:
La Trobe UniversityBundoora VIC 3083Australia e-mail: davey@latcs1.lat.oz.au
R. W. Quackenbush
Affiliation:
University of ManitobaWinnipeg ManitobaCanadaR3T 2N2 e-mail: qbush@ccu.umanitoba.ca
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Abstract

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A strong, natural duality is established for the variety by a dihedral gruop of order 2m with m odd. This is the first natural duality for a non-abelian variety of groups.

Keywords

dualitynatural dualitystrong dualitygroupdihedral groupvariety

MSC classification

Secondary: 08A02: Relational systems, laws of composition 08B05: Equational logic, Mal′cev (Mal′tsev) conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 216 - 228
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Clark, D. M. and Davey, B. A., ‘The quest for strong dualities’, J. Austral. Math. Soc. (Series A) 58 (1995),248–280.Google Scholar
[2]Clark, D. M. and Davey, B. A., ‘When is a natural duality ‘good’?’, Algebra Universalis 35 (1996), 237–267.Google Scholar
[3]Clark, D. M. and Davey, B. A., ‘Natural dualities for the working algebraist’, in preparation.Google Scholar
[4]Davey, B. A., ‘Duality theory on ten dollars a day’, in: Algebras and orders (Rosenberg, I. G. and Sabidussi, G. eds), NATO Advanced Study Institute Series, Series C, Vol. 389 (Kluwer, 1993) pp. 71–111.Google Scholar
[5]Davey, B. A., ‘Dualizability of finite abelian groups and some other finite algebras’, preprint, 1994.Google Scholar
[6]Davey, B. A. and Werner, H., ‘Dualities and equivalences for varieties of algebras’, in: Contributions to lattice theory (Szeged, 1980), (Huhn, A. P. and Schmidt, E. T., eds.) Colloq. Math. Soc. János Bolyai, Vol. 33 (North-Holland, Amsterdam, 1983), pp. 101–275.Google Scholar
[7]Kovács;, L. G., ‘Free groups in a dihedral variety’, Proc. Roy. lrish Acad. 89A (1989), 115–117.Google Scholar
[8]Neumann, H., Varieties of groups, Ergebnisse der Mathematik und ihrer Grenzgebeite 37 (Springer, Berlin, 1967).Google Scholar