This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying such where automorphism group is an almost simple with socle alternating or sporadic group, and classical a vertex-stabiliser acting faithfully on set neighbours.

We show that the concept of strong Noether position for a polynomial ideal I CP is equivalent to δ-regularity and thus related to Pommaret bases. In particular, we provide explicit Pommaret bases for two of the ideal sequences used in Hashemi’s definition of strong Noether position and alternative proofs for a number of his statements. Finally, we show that one consequence of δ-regularity is th...

Based on Kleshchev's branching theorems for the p-modular irreducible representations of the symmetric group and on the recent proof of the Mullineux Conjecture, we investigate in this article the corresponding branching problem for the p-modular irreducible representations of the alternating group A n. We obtain information on the socle of the restrictions of such A n-representations to A n?1 ...

We investigate finite elation Laguerre planes admitting a group of automorphisms that is two-transitive on the set of generators. We exclude the sporadic cases of socles in two-transitive groups, as well as the cases with abelian socle (except for the smallest ones, where the Laguerre planes are Miquelian of order at most four). The remaining cases are dealt with in a separate paper. As a conse...

It is unknown if an Artinian level O-sequence of codimension 3 and type r (≥ 2) is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra A of codimension 3 has the Hilbert function H : h0 h1 · · · hd−1 hd · · · hd }...