Finite vertex-primitive edge-transitive metacirculants

Li, Cai Heng; Lu, Zai Ping; Pan, Jiangmin

doi:10.1007/s10801-014-0507-8

Cited by 10 publications

(2 citation statements)

References 33 publications

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“…Factorizations of almost simple groups have many natural applications, especially when combined with the O'Nan-Scott Theorem, which describes the structure and action of finite primitive permutation groups. For example, see [2,17,23,24] for related work on primitive groups containing transitive subgroups with prescribed properties, and we refer the reader to [18,22] for applications to the study of Cayley graphs.…”

Section: Introductionmentioning

confidence: 99%

On solvable factors of almost simple groups

Burness¹,

Li²

2019

Preprint

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Let G be a finite almost simple group with socle G0. A (nontrivial) factorization of G is an expression of the form G = HK, where the factors H and K are core-free subgroups. There is an extensive literature on factorizations of almost simple groups, with important applications in permutation group theory and algebraic graph theory. In a recent paper, Li and Xia describe the factorizations of almost simple groups with a solvable factor H. Several infinite families arise in the context of classical groups and in each case a solvable subgroup of G0 containing H ∩ G0 is identified. Building on this earlier work, in this paper we compute a sharp lower bound on the order of a solvable factor of every almost simple group and we determine the exact factorizations with a solvable factor. As an application, we describe the finite primitive permutation groups with a nilpotent regular subgroup, extending classical results of Burnside and Schur on cyclic regular subgroups, and more recent work of Li in the abelian case.

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Section: Introductionmentioning

confidence: 99%

On solvable factors of almost simple groups

Burness¹,

Li²

2019

Preprint

Self Cite

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“…The class of metacirculants provides a rich source of many interesting families of graphs and has been extensively studied. For example, some special edge-transitive metacirculants have been characterised (see [12,14] for circulants, [5,21] for the case of order a product of two primes, [18] for the case of prime-power order, [15] for the vertex-primitive case and [17,24] for the case of Frobenius metacirculants with small valency). Moreover, an infinite family of arc-regular dihedrants of any prescribed valency is constructed in [11] and arc-regular dihedrants of prime valency are classified in [7].…”

Section: Introductionmentioning

confidence: 99%