Mostrar el registro sencillo del ítem
dc.contributor.author | Beltrán Felip, Antonio | es_ES |
dc.contributor.author | Felipe Román, María José | es_ES |
dc.contributor.author | Melchor, Carmen | es_ES |
dc.date.accessioned | 2023-07-03T18:01:21Z | |
dc.date.available | 2023-07-03T18:01:21Z | |
dc.date.issued | 2022-12 | es_ES |
dc.identifier.issn | 1660-5446 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/194638 | |
dc.description.abstract | [EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian simple group. We demonstrate that, in fact, < A > = < B > is solvable, the elements of A and B are p-elements for some prime p, and < A > is p-nilpotent. Moreover, under the second assumption, it turns out that A = B. This research is done by appealing to recently developed techniques and results that are based on the Classification of Finite Simple Groups. | es_ES |
dc.description.sponsorship | The authors thank the referee for careful reading that helped to improve the manuscript. This research is partially supported by Ministerio de Ciencia, Innovacion y Universidades, Proyecto PGC2018-096872-B-I00 and by Generalitat Valenciana, Proyecto CIAICO/2021/163. The first-named author is also supported by the National Nature Science Fund of China (No. 12071181) and by Proyecto UJI-B2019-03. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Springer-Verlag | es_ES |
dc.relation.ispartof | Mediterranean Journal of Mathematics | es_ES |
dc.rights | Reconocimiento (by) | es_ES |
dc.subject | Conjugacy classes | es_ES |
dc.subject | Products of conjugacy classes | es_ES |
dc.subject | Solvability criterium | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | An Arad and Fisman's theorem on products of conjugacy classes revisited | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1007/s00009-022-02171-7 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-096872-B-I00/ES/GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/Conselleria d'Educació, Investigació, Cultura i Esport de la Generalitat Valenciana//CIAICO%2F2021%2F163//Representaciones y clases de conjugación en grupos finitos: estructura local-global/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/NSFC//12071181/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/UJI//UJI-B2019-03/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI//PGC2018-096872-B-I00//GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros Industriales - Escola Tècnica Superior d'Enginyers Industrials | es_ES |
dc.description.bibliographicCitation | Beltrán Felip, A.; Felipe Román, MJ.; Melchor, C. (2022). An Arad and Fisman's theorem on products of conjugacy classes revisited. Mediterranean Journal of Mathematics. 19(6):1-12. https://doi.org/10.1007/s00009-022-02171-7 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1007/s00009-022-02171-7 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 12 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 19 | es_ES |
dc.description.issue | 6 | es_ES |
dc.relation.pasarela | S\457929 | es_ES |
dc.contributor.funder | Universitat Jaume I | es_ES |
dc.contributor.funder | Agencia Estatal de Investigación | es_ES |
dc.contributor.funder | National Natural Science Foundation of China | es_ES |
dc.contributor.funder | Conselleria d'Educació, Investigació, Cultura i Esport de la Generalitat Valenciana | es_ES |
dc.description.references | Arad, Z., Fisman, E.: An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups. Proc. Edinb. Math. Soc. 30, 7–22 (1987) | es_ES |
dc.description.references | Arad, Z., Fisman, E., Muzychuk, M.: Order evaluation of products of subsets in finite groups and its applications. I. J. Algebra 182(3), 577–603 (1996) | es_ES |
dc.description.references | Arad, Z., Muzychuk, M.: Order evaluation of products of subsets in finite groups and its applications. II. Trans. Am. Math. Soc. 349(11), 4401–4414 (1997) | es_ES |
dc.description.references | Beltrán, A., Camina, R.D., Felipe, M.J., Melchor, C.: Powers of conjugacy classes in a finite group. Ann. Mat. Pura Appl. 199(2), 409–424 (2020) | es_ES |
dc.description.references | Beltrán, A., Felipe, M.J., Melchor, C.: Multiplying a conjugacy class by its inverse in a finite group. Isr. J. Math. 227(2), 811–825 (2018) | es_ES |
dc.description.references | Beltrán, A., Felipe, M.J., Melchor, C.: Squares of real conjugacy classes in finite groups. Ann. Mat. Pura Appl. 197(2), 317–328 (2018) | es_ES |
dc.description.references | Camina, R.D.: Applying combinatorial results to products of conjugacy classes. J. Group Theory 23(5), 917–923 (2020) | es_ES |
dc.description.references | Guralnick, R.M., Navarro, G.: Squaring a conjugacy class and cosets of normal subgroups. Proc. Am. Math. Soc. 144(5), 1939–1945 (2016) | es_ES |
dc.description.references | Huppert, B.: Character Theory of Finite Groups. Walter de Gruyter, Berlin (1998) | es_ES |
dc.description.references | The GAP Group, GAP-Groups, Algorithms and Programming, Vers. 4.7.7 (2015). http://ww.gap-system.org | es_ES |