Let M be a Minkowski plane and let G be the automorpphism gropup of M. A set I of points of M is said to be regular if the identity is the unique automorphism of G mapping I onto itself. The set I is called a IR-set if it is a regular set of independent points. We prove that each known finite Minkoeski plane contain IR-stes except for the planes of order 4, 4 and 7 respectively. We find all the non-equivalent IR-sets contained in the known Minkowski planes of order 8 and 9 respectively.
Regular sets of points in finite Minkowski planes / Rinaldi, Gloria; F., Zironi. - In: ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1126-8042. - STAMPA. - 9:(2001), pp. 33-44.
Regular sets of points in finite Minkowski planes
RINALDI, Gloria;
2001
Abstract
Let M be a Minkowski plane and let G be the automorpphism gropup of M. A set I of points of M is said to be regular if the identity is the unique automorphism of G mapping I onto itself. The set I is called a IR-set if it is a regular set of independent points. We prove that each known finite Minkoeski plane contain IR-stes except for the planes of order 4, 4 and 7 respectively. We find all the non-equivalent IR-sets contained in the known Minkowski planes of order 8 and 9 respectively.
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