Half-automorphisms of simple Moufang loops
| Autor: | Maria de Lourdes Merlini Giuliani, Stephen M. Gagola |
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| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Algebra and Number Theory 010102 general mathematics Multiplicative function Automorphism 01 natural sciences Combinatorics Mathematics::Group Theory Simple (abstract algebra) 0103 physical sciences Bijection Order (group theory) 010307 mathematical physics 0101 mathematics Moufang loop Mathematics |
| Zdroj: | Journal of Algebra. 546:27-36 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2019.10.032 |
| Popis: | A half-isomorphism φ : G → K between multiplicative systems G and K is a bijection from G onto K such that φ ( a b ) ∈ { φ ( a ) φ ( b ) , φ ( b ) φ ( a ) } for any a , b ∈ G . For groups all half-isomorphisms are either isomorphisms or anti-isomorphisms as shown by W.R. Scott (1957) [14] . Scott's result carries over to certain classes of Moufang loops including Moufang loops of odd order. The class of loops considered here are Paige loops, namely the class of finite nonassociative simple Moufang loops. In this paper, it is shown that any half-automorphism of a finite simple Moufang loop is either an automorphism are an anti-automorphism, thus extending Scott's result. |
| Databáze: | OpenAIRE |
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