| Texto completo | |
| Autor(es): |
Goncalves, Daciberg Lima
;
Guaschi, John
;
Ocampo, Oscar
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 474, p. 393-423, MAR 15 2017. |
| Citações Web of Science: | 2 |
| Resumo | |
Let n >= 3. In this paper, we study the quotient group B-n/{[}P-n,P-n] of the Artin braid group Bn by the commutator subgroup of its pure Artin braid group P-n. We show that B-n/{[}P-n,P-n] is a crystallographic group, and in the case n = 3, we analyse explicitly some of its subgroups. We also prove that Bn/{[}P-n,P-n] possesses torsion, and we show that there is a one-to-one correspondence between the conjugacy classes of the finite-order elements of B-n/{[}P-n,P-n] with the conjugacy classes of the elements of odd order of the symmetric group S-n, and that the isomorphism class of any Abelian subgroup of odd order of Sn is realised by a subgroup of B-n/{[}p(n),p(n)] Finally, we discuss the realisation of non-Abelian subgroups of Sn of odd order as subgroups of B-n/{[}P-n,P-n] , and we show that the Frobenius group of order 21, which is the smallest non-Abelian group of odd order, embeds in B-n/{[}P-n,P-n] for all n >= 7. (C) 2016 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 08/58122-6 - Grupos brunnianos de tranças |
| Beneficiário: | Oscar Eduardo Ocampo Uribe |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |