On some subgroups of the multiplicative group of finite rings
نویسنده
چکیده
Let S be a subset of Fq, the field of q elements and h ∈ Fq[x] a polynomial of degree d > 1 with no roots in S. Consider the group generated by the image of {x − s | s ∈ S} in the group of units of the ring Fq[x]/(h). In this paper we present a number of lower bounds for the size of this group. Our main motivation is an application to the recent polynomial time primality testing algorithm [AKS]. The bounds have also applications to graph theory and to the bounding of the number of rational points on abelian covers of the projective line over finite fields.
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