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On transitive commutative idempotent quasigroups

Part of: Other generalizations of groups Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Arnold Neumaier
Arnold Neumaier
Affiliation:
Fachbereich Mathematik Technische Universität D-1000 Berlin 12 West Germany
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Abstract

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Commutative idempotent quasigroups with a sharply transitive automorphism group G are described in terms of so-called Room maps of G. Orthogonal Room maps and skew Room maps are used to construct Room squares and skew Room squares. Very general direct and recursive constructions for skew Room maps lead to the existence of skew Room maps of groups of order prime to 30. Also some nonexistence results are proved.

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares 20N05: Loops, quasigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 411 - 429
Copyright
Copyright © Australian Mathematical Society 1979

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