The multiplicative loops of Jha-Johnson semifields

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 ar...

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Bibliographic Details
Main Author: Pumpluen, Susanne
Format: Article
Language:English
Published: American Mathematical Society 2019
Online Access:https://eprints.nottingham.ac.uk/49292/
Description
Summary: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 qnm -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.