The multiplicative loops of Jha-Johnson semifields

Abstract

The multiplicative loops of Jha-Johnson semifields are non-automorphic finite loops whose left and right nuclei are the multiplicative groups of a field extension of their centers.They yield examples of finite loops with non-trivial automorphism group and non-trivial inner mappings.Upper bounds are given for the number of non-isotopic multiplicative loops of order q nm -1 that are defined using the twisted polynomial ring K[t; σ] and a twisted irreducible polynomial of degree m, when the automorphism σ has order n.

Locations

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