## Illinois Journal of Mathematics

- Illinois J. Math.
- Volume 47, Number 1-2 (2003), 461-475.

### Finite transitive permutation groups and bipartite vertex-transitive graphs

#### Abstract

We prove a structure theorem for a class of finite transitive permutation groups that arises in the study of finite bipartite vertex-transitive graphs. The class consists of all finite transitive permutation groups such that each non-trivial normal subgroup has at most two orbits, and at least one such subgroup is intransitive. The theorem is analogous to the O'Nan-Scott Theorem for finite primitive permutation groups, and this in turn is a refinement of the Baer Structure Theorem for finite primitive groups. An application is given for arc-transitive graphs.

#### Article information

**Source**

Illinois J. Math., Volume 47, Number 1-2 (2003), 461-475.

**Dates**

First available in Project Euclid: 17 November 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.ijm/1258488166

**Digital Object Identifier**

doi:10.1215/ijm/1258488166

**Mathematical Reviews number (MathSciNet)**

MR2031334

**Zentralblatt MATH identifier**

1032.20004

**Subjects**

Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

#### Citation

Praeger, Cheryl E. Finite transitive permutation groups and bipartite vertex-transitive graphs. Illinois J. Math. 47 (2003), no. 1-2, 461--475. doi:10.1215/ijm/1258488166. https://projecteuclid.org/euclid.ijm/1258488166