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Vertex-transitive tournaments of order a product of two distinct primes
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Jing Xu
Veröffentlicht/Copyright:
8. Februar 2010
Abstract
In this paper, we begin a classification of the vertex-transitive tournaments of order pq where p and q are distinct odd primes. In particular we characterize the pq-circulant tournaments; see Theorem 4.3. Moreover, we determine 2-closed (in Wielandt's sense) odd-order transitive permutation groups of degree p and pq by using the classifications of vertex-transitive tournaments of order p and pq. We prove that each such 2-closed group containing a cyclic regular subgroup is the full automorphism group of some circulant tournament.
Received: 2009-08-12
Revised: 2009-10-13
Published Online: 2010-02-08
Published in Print: 2010-July
© de Gruyter 2010
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Artikel in diesem Heft
- A note on the Green theory in the Clifford-theoretic context of a defect zero p-block of a normal subgroup of a finite group
- A note on a conjecture of K. Harada and strongly p-embedded Frobenius subgroups
- Carter–Payne homomorphisms and branching rules for endomorphism rings of Specht modules
- Some linear actions of finite groups with q′-orbits
- Semi-rational solvable groups
- Finite non-abelian 2-groups such that any two distinct minimal non-abelian subgroups have cyclic intersection
- A note on the p-supersolvability of finite groups
- Vertex-transitive tournaments of order a product of two distinct primes
- On the derived length of the unit group of a group algebra
- On the subgroups with non-trivial Möbius number
- Subgroups of free groups and primitive elements
- Small index subgroups of the mapping class group
