Cyclic extensions of finite simple groups
| Autor: | Stephen M. Gagola, Alexander N. Grishkov |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1435-4446 1433-5883 |
| DOI: | 10.1515/jgth-2016-0039 |
| Popis: | Here cyclic extensions, not necessarily split, of simple groups are looked at. It is shown that if N is a finite simple group that is either an abelian group, an alternating group, a Suzuki group, a projective special linear group or a sporadic simple group and G = 〈 N , u 〉 ${G=\langle N,u\rangle}$ is a cyclic extension of N resulting in a Moufang loop, then 〈 N , u 2 〉 ${\langle N,u^{2}\rangle}$ is a group. Moreover, if G is nonassociative, then G is a generalization of the Chein loop where u inverts all of the elements of N. |
| Databáze: | OpenAIRE |
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