Soient le groupe de tresses virtuelles à brins et le groupe symétrique de l’ensemble à éléments. Soient tels que , et . Nous déterminons tous les homomorphismes de dans , de dans et de dans . Comme corollaires nous obtenons que est isomorphe à et que est à la fois hopfien et co-hofpien.
Let be the virtual braid group on strands and let be the symmetric group on letters. Let such that , and . We determine all possible homomorphisms from to , from to and from to . As corollaries we get that is isomorphic to and that is both, Hopfian and co-Hofpian.
Accepté le : 2019-05-21
Publié le : 2020-12-18
Classification : 20F36, 20E36
Mots clés : groupe de tresses virtuelles, théorie de Bass–Serre, groupe d’Artin, groupe symétrique, produit amalgamé
@article{AIF_2020__70_3_1341_0, author = {Bellingeri, Paolo and Paris, Luis}, title = {Virtual braids and permutations}, journal = {Annales de l'Institut Fourier}, pages = {1341--1362}, publisher = {Association des Annales de l'institut Fourier}, volume = {70}, number = {3}, year = {2020}, doi = {10.5802/aif.3336}, language = {en}, url = {aif.centre-mersenne.org/item/AIF_2020__70_3_1341_0/} }
Bellingeri, Paolo; Paris, Luis. Virtual braids and permutations. Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 1341-1362. doi : 10.5802/aif.3336. https://aif.centre-mersenne.org/item/AIF_2020__70_3_1341_0/
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