Friday, Mar 3, 2017 - 3:00pm - Allen 411
ACT seminar
On automorphism groups of deleted wreath products
Dr. Ted Dobson, Mathematics, Msstate

Title:  On automorphism groups of deleted wreath products
  (2nd part of a 2 part talk; abstract from last week's 1st part is below.)

Abstract:  Let Γ1 and Γ2 be digraphs. The deleted wreath product of Γ1 and Γ2, denoted Γ1d Γ2, is the digraph with vertex set V(Γ1) × V(Γ2) and arc set {((x1y1)(x2y2)) : (x1x2) ∈ A(Γ1) and y1y2 or x1 = x2 and (y1y2) ∈ A(Γ2)}. We study the automorphism group of Γ1d Γ2, and amongst other things, show that if Γ is a vertex-transitive digraph and n a positive integer such that n  > |V(Γ)|, then Aut(Γd Kn) = Aut(Γ) × Sn with an explicit list of exceptions (here Kn is the complement of the complete graph). As a corollary, we show that if in addition Γ is 1/2-transitive, then Γd Kn is also 1/2-transitive. This is joint work with Stefko Miklavič and Primož Šparl.

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