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An Arad and Fisman's theorem on products of conjugacy classes revisited

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An Arad and Fisman's theorem on products of conjugacy classes revisited

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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
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dc.description.references The GAP Group, GAP-Groups, Algorithms and Programming, Vers. 4.7.7 (2015). http://ww.gap-system.org es_ES


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