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Tetravalent Arc-Transitive Graphs of Order 3p 2

Mohsen Ghasemi (2014)

Discussiones Mathematicae Graph Theory

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given

The classification of finite groups by using iteration digraphs

Uzma Ahmad, Muqadas Moeen (2016)

Czechoslovak Mathematical Journal

A digraph is associated with a finite group by utilizing the power map f : G G defined by f ( x ) = x k for all x G , where k is a fixed natural number. It is denoted by γ G ( n , k ) . In this paper, the generalized quaternion and 2 -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2 -group are determined for a 2 -group to be a generalized quaternion group. Further, the classification of two generated 2 -groups as abelian or non-abelian...

The local lifting problem for actions of finite groups on curves

Ted Chinburg, Robert Guralnick, David Harbater (2011)

Annales scientifiques de l'École Normale Supérieure

Let k be an algebraically closed field of characteristic p > 0 . We study obstructions to lifting to characteristic 0 the faithful continuous action φ of a finite group G on k [ [ t ] ] . To each such  φ a theorem of Katz and Gabber associates an action of G on a smooth projective curve Y over k . We say that the KGB obstruction of φ vanishes if G acts on a smooth projective curve X in characteristic  0 in such a way that X / H and Y / H have the same genus for all subgroups H G . We determine for which G the KGB obstruction...

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