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Single laws for two subvarieties of squags

Published online by Cambridge University Press:  17 April 2009

Diane Donovan
Diane Donovan
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
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Abstract

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We give single laws for two subvarieties of Steiner quasigroups (squags); the subvariety of squags whose underlying triple systems are the affine spaces over GF[3], and the subvariety of squags whose underlying triple systems are the affine triple systems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 157 - 165
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Donovan, Diane and Oates-Williams, Sheila, ‘Single laws for sloops and squags’, Discrete Math, (to appear).Google Scholar
[2]Ganter, B. and Werner, H., ‘Co-ordinatizing Steiner systems’, Ann. Discrete Math. 7 (1980), 3–24.CrossRefGoogle Scholar
[3]Macdonald, Sheila Oates, ‘A characterisation of affine triple systems’, Ars Combin. 2 (1976), 23–24.Google Scholar
[4]Young, H. Peyton, ‘Affine triple systems and Matroid Designs’, Math. Z. 132 (1973), 343–359.CrossRefGoogle Scholar