Primož Potočnik: Non-semiregular abelian normal subgroups in arc-transitive groups and PX graphs

Povzetek. When analysing graphs admitting an arc-transitive group G, it is often helpful to distinguish the cases when G has and when G does not have a nontrivial abelian normal subgroup. If it doesn’t, then the structure of G is very restricted. If it does, then either

(1) the abelian normal subgroup is semiregular, in which case the quotenting technique yields a reduction to a smaller arc-transitive graph of which the original one is a regular abelian cover;

(2) the abelian normal subgroup is not semiregular.

In my seminar, I will discuss the situation when (2) occurs. In particular, I will show how this case yields a complete classification of the corresponding graphs in the case of valence 4.