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Tetravalent half-arc-transitive graphs of order $p^{2} q^{2}$

Hailin Liu, Bengong Lou, Bo Ling (2019)

Czechoslovak Mathematical Journal

We classify tetravalent $G$ -half-arc-transitive graphs $Γ$ of order $p^{2} q^{2}$ , where $G \leq 𝖠𝗎𝗍 Γ$ and $p$ , $q$ are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.

The irreducibility of compositions of linear polynomials over a finite field

S. D. Cohen (1982)

Compositio Mathematica

The Primitive Permutation Groups of Some Special Degrees, II: Small Multiples of Certain Large Primes.

Peter M. Neumann, Jan Saxl (1979)

Mathematische Zeitschrift

Théorèmes sur les groupes primitifs.

Jordan, Camille (1871)

Journal de Mathématiques Pures et Appliquées

V-кольца и их связь с группами автоморфизмов бинарных отношений

М.Х. Клин (1972)

Matematiceskie issledovanija

Weakly-exceptional quotient singularities

Dmitrijs Sakovics (2012)

Open Mathematics

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.