Algebraic Graph Theory International Webinar (13.4.2021)
v utorok 13.4.2021 o 19:00 hod.
Od: Róbert Jajcay
The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on April 13, 2021, at 7pm Central European Time, for the next presentation delivered by Tom Tucker.
He will speak on Recognizing vertex-transitive digraphs which are wreath products, double coset digraphs, and generalized wreath products
It is known that a Cayley digraph $\Cay(A,S)$ of an abelian group $A$ is isomorphic to a nontrivial wreath product if and only if there is a proper nontrivial subgroup $B\le A$ such that $S\setminus B$ is a union of cosets of $B$ in $A$. We generalize this result to Cayley digraphs $\Cay(G,S)$ of nonabelian groups $G$ by showing that such a digraph is isomorphic to a nontrivial wreath product if and only if there is a proper nontrivial subgroup $H\le G$ such that $S\setminus H$ is a union of double cosets of $H$ in $G$. This result is proven in the more general situation of a double coset digraph. We then give applications of this result, which include showing the problem of determining automorphism groups of vertex-transitive digraphs is equivalent to the problem of determining automorphism groups of Cayley digraphs, and extending the definition of generalized wreath product digraphs to double coset digraphs of all groups $G$.
Join Zoom Meeting at
Meeting ID: 925 4558 6220
Further details may be found at euler.doa.fmph.uniba.sk/AGTIW.html where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.
Hoping to see you at the webinar, and wishing you all the best.