Quaternionic Starters |
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| Authors: | Arrigo Bonisoli Gloria Rinaldi |
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| Affiliation: | (1) Dipartimento di Scienze Sociali, Cognitive e Quantitative, Università di Modena e Reggio Emilia, via Giglioli Valle 9, 42100 Reggio Emilia, Italy;(2) Dipartimento di Scienze Agrarie, Università di Modena e Reggio Emilia, via Kennedy 17, 42100 Reggio Emilia, Italy |
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| Abstract: | Let m be an integer, m  2 and set n = 2m. Let G be a non-cyclic group of order 2n admitting a cyclic subgroup of order n. We prove that G always admits a starter and so there exists a one–factorization  of K2n admitting G as an automorphism group acting sharply transitively on vertices. For an arbitrary even n > 2 we also show the existence of a starter in the dicyclic group of order 2n.Research performed within the activity of INdAM–GNSAGA with the financial support of the Italian Ministry MIUR, project  Strutture Geometriche, Combinatoria e loro Applicazioni |
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| Keywords: | One-factorization Sharply transitive permutation group Starter |
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