# Events

### 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 *Γ*_{1} and *Γ*_{2} be digraphs. The *deleted wreath product of Γ_{1} and Γ_{2}*, denoted

*Γ*

_{1}≀

_{d}

*Γ*

_{2}, is the digraph with vertex set

*V*(

*Γ*

_{1}) ×

*V*(

*Γ*

_{2}) and arc set {((

*x*

_{1},

*y*

_{1})(

*x*

_{2},

*y*

_{2})) : (

*x*

_{1},

*x*

_{2}) ∈

*A*(

*Γ*

_{1}) and

*y*

_{1}≠

*y*

_{2}or

*x*

_{1}=

*x*

_{2}and (

*y*

_{1},

*y*

_{2}) ∈

*A*(

*Γ*

_{2})}. We study the automorphism group of

*Γ*

_{1}≀

_{d}

*Γ*

_{2}, 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(

*Γ*≀

_{d}

*K*

_{n}) = Aut(

*Γ*) ×

*S*

_{n}with an explicit list of exceptions (here

*K*

_{n}is the complement of the complete graph). As a corollary, we show that if in addition

*Γ*is 1/2-transitive, then

*Γ*≀

_{d}

*K*

_{n}is also 1/2-transitive. This is joint work with Stefko Miklavič and Primož Šparl.