Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897543 | Journal of Pure and Applied Algebra | 2018 | 22 Pages |
Abstract
We show how to construct all the extensions of left braces by ideals with trivial structure. This is useful to find new examples of left braces. But, to do so, we must know the basic blocks for extensions: the left braces with no ideals besides the trivial and the total ideal, called simple left braces. In this article, we present the first non-trivial examples of finite simple left braces. To explicitly construct them, we define the matched product of two left braces, which is a useful method to recover a finite left brace from its Sylow subgroups.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David Bachiller,