The multiplicative loops of Jha-Johnson semifields

Pumpluen, Susanne

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 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.

Citation

Pumpluen, S. (2019). The multiplicative loops of Jha-Johnson semifields. Communications in Contemporary Mathematics, 721, 227-242

• Journal Article Type: Article
• Acceptance Date: Jan 23, 2018
• Publication Date: Jan 12, 2019
• Deposit Date: Jan 23, 2018
• Publicly Available Date: Jan 12, 2019
• Journal: Contemporary Mathematics
• Print ISSN: 0219-1997
• Electronic ISSN: 1793-6683
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 721
• Pages: 227-242
• Public URL: https://nottingham-repository.worktribe.com/output/906298
• Related Public URLs: https://www.ams.org/books/conm/721/
• Contract Date: Aug 2, 2018