Abstract
In this paper, we mainly study the orbital graphs of primitive groups with the socle A7 x A7 which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7, then we discuss the stabilizer of two points in A7. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.
Highlights
We mainly study the orbital graphs of primitive groups with the socle A7 × A7 which acts by diagonal action
Let G be a primitive group with the socle A7 × A7, and T = A= 7, H {(t,t ) | t ∈T}
In 1964, Wielandt’s book referred that if G is a finite primitive group with a suborbit of length 2, G is a dihedral group of order 2q (q prime) [1]
Summary
We mainly study the orbital graphs of primitive groups with the socle A7 × A7 which acts by diagonal action. Let G be a primitive group with the socle A7 × A7 , and T = A= 7 , H {(t,t ) | t ∈T} . Let G be a group acting transitively on a set Ω. There are many papers which refer to the suborbits of primitive group.
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