Suzuki Group and Flag-Transitive Point-Primitive 2-（ν，Κ，λ）Designs

Given a factor code ${\it\pi}$ from a shift of finite type $X$ onto a sofic shift $Y$, the class degree of ${\it\pi}$ is defined to be the minimal number of transition classes over the points of $Y$. In this paper, we investigate the structure of transition classes and present several dynamical properties analogous to the properties of fibers of finite-to-one factor codes. As a corollary, we show that for an irreducible factor triple, there cannot be a transition between two distinct transition classes over a right transitive point, answering a question raised by Quas.

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Flag-transitive point-quasiprimitive automorphism groups of 2-designs with λ≤4

Discrete Mathematics ◽

10.1016/j.disc.2018.10.027 ◽

2019 ◽

Vol 342 (2) ◽

pp. 427-432

Author(s):

Zhilin Zhang ◽

Shenglin Zhou

Keyword(s):

Automorphism Groups ◽

Transitive Point

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Line-transitive, point quasiprimitive automorphism groups of finite linear spaces are affine or almost simple

Aequationes Mathematicae ◽

10.1007/s000100050174 ◽

2001 ◽

Vol 61 (3) ◽

pp. 221-232 ◽

Cited By ~ 17

Author(s):

A. R. Camina ◽

C. E. Praeger

Keyword(s):

Automorphism Groups ◽

Linear Spaces ◽

Transitive Point ◽

Finite Linear

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Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

Journal of Algebra and Its Applications ◽

10.1142/s0219498817501109 ◽

2017 ◽

Vol 16 (06) ◽

pp. 1750110

Author(s):

Haiyan Guan ◽

Shenglin Zhou

Keyword(s):

Linear Space ◽

Automorphism Groups ◽

Linear Spaces ◽

Finite Linear Space ◽

Transitive Point ◽

Finite Linear

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let [Formula: see text] be a non-trivial finite linear space with [Formula: see text] points, where [Formula: see text] and [Formula: see text] are two primes. We prove that if [Formula: see text] is line-transitive point-imprimitive, then [Formula: see text] is solvable.

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