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A note on simple medial quasigroups

K. K. Ščukin (1993)

Commentationes Mathematicae Universitatis Carolinae

A solvable primitive group with finitely generated abelian stabilizers is finite.

A note on solvable vertex stabilizers of s -transitive graphs of prime valency

Song-Tao Guo, Hailong Hou, Yong Xu (2015)

Czechoslovak Mathematical Journal

A graph X , with a group G of automorphisms of X , is said to be ( G , s ) -transitive, for some s 1 , if G is transitive on s -arcs but not on ( s + 1 ) -arcs. Let X be a connected ( G , s ) -transitive graph of prime valency p 5 , and G v the vertex stabilizer of a vertex v V ( X ) . Suppose that G v is solvable. Weiss (1974) proved that | G v | p ( p - 1 ) 2 . In this paper, we prove that G v ( p m ) × n for some positive integers m and n such that n div m and m p - 1 .

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