Some Properties of Automorphism Groups of Paving Matroids

This paper deals with the relation between the automorphism groups of some paving matroids and Z3, where Z3 is the additive group of modulo 3 over Z. It concludes that for paving matroids under most cases, Z3 is not isomorphic to the automorphism groups of these paving matroids. Even in the exceptional cases, we reasonably conjecture that Z3 is not isomorphic to the automorphism groups of the corresponding paving matroids. Actually, the result here is relative to the Welsh’s open problem that for any group G, there is a paving matroid with automorphism group isomorphic to G.