Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants

Song, Shu Jiao; Li, Cai Heng; Zhang, Hua

doi:10.1016/j.jalgebra.2013.10.022

Cited by 5 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then G is isomorphic to a subgroup of Aut(G + ), and thus G has a unique minimal normal subgroup, which is soc(G + ) and has exactly two orbits. Thus G is a bi-quasiprimitive d-group, and by [22,Theorem 1.1], one of parts (3)-( 5) holds.…”

Section: And Sincementioning

confidence: 96%

“…Although the primitivity implies the quasiprimitivity, the bi-primitivity and the bi-quasiprimitivity are independent. Bi-quasiprimitive dgroups have been classified in [22]. The following proposition determines bi-primitive d-groups.…”

Section: Bi-primitive D-groupsmentioning

confidence: 99%

“…Wielandt proved that primitive d-groups are 2-transitive, refer to [23], extended Schur's result regarding c-groups to d-groups. Then in [16,21,22], quasiprimitive d-groups and bi-quasiprimitive d-groups are classified. The main theorem of this paper gives a recursive characterization of d-groups.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite permutation groups containing a regular dihedral subgroup

Song¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: And Sincementioning

confidence: 96%

Section: Bi-primitive D-groupsmentioning

confidence: 99%

See 1 more Smart Citation

Finite permutation groups containing a regular dihedral subgroup

Song¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, if , then G is usually omitted in the previous notation. The first remarkable result about the class of finite -arc-transitive graphs comes from Tutte [36, 37]. Due to the influence of Tutte’s work, this class of graphs has been studied extensively in the literature (see [1, 17, 26, 32]).…”

Section: Preliminariesmentioning

confidence: 99%

Finite Two-Distance-Transitive Dihedrants

Jin

Tan²

2022

J. Aust. Math. Soc.

View full text Add to dashboard Cite

A noncomplete graph is $2$ -distance-transitive if, for $i \in \{1,2\}$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance i in the graph, there exists an element of the graph automorphism group that maps $(u_1,v_1)$ to $(u_2,v_2)$ . This paper determines the family of $2$ -distance-transitive Cayley graphs over dihedral groups, and it is shown that if the girth of such a graph is not $4$ , then either it is a known $2$ -arc-transitive graph or it is isomorphic to one of the following two graphs: $ {\mathrm {K}}_{x[y]}$ , where $x\geq 3,y\geq 2$ , and $G(2,p,({p-1})/{4})$ , where p is a prime and $p \equiv 1 \ (\operatorname {mod}\, 8)$ . Then, as an application of the above result, a complete classification is achieved of the family of $2$ -geodesic-transitive Cayley graphs for dihedral groups.

show abstract

“…Constructing and characterizing half-symmetric graphs is an active topic in symmetrical graph theory which has received considerable attention, see for example [9,10,12,15]. The following result provides a generic method for constructing halfsymmetric graphs as subnormal Cayley graphs, which is proved in Section 4.…”

Section: Introductionmentioning

confidence: 96%