The problem of extending (sharply) k-transitive permutation sets into (sharply) (k+1)-transitive permutation sets is studied. We give sufficient conditions for the extension. These conditions reduce to a unique necessary one in case the starting set is a group. Furthermore we establis some necessary and sufficient condition for a sharply k-transitive permutation sets (k>=3) to be a group.
Exstension of multiply transitive permutation sets / Rinaldi, Gloria; S., Spaggiari. - In: RESULTS IN MATHEMATICS. - ISSN 1422-6383. - STAMPA. - 32:(1997), pp. 95-99.
Exstension of multiply transitive permutation sets
RINALDI, Gloria;
1997-01-01
Abstract
The problem of extending (sharply) k-transitive permutation sets into (sharply) (k+1)-transitive permutation sets is studied. We give sufficient conditions for the extension. These conditions reduce to a unique necessary one in case the starting set is a group. Furthermore we establis some necessary and sufficient condition for a sharply k-transitive permutation sets (k>=3) to be a group.
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