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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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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

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Título: An Arad and Fisman's theorem on products of conjugacy classes revisited
Autor: Beltrán Felip, Antonio Felipe Román, María José Melchor, Carmen
Entidad UPV: Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros Industriales - Escola Tècnica Superior d'Enginyers Industrials
Fecha difusión:
Resumen:
[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 ...[+]
Palabras clave: Conjugacy classes , Products of conjugacy classes , Solvability criterium
Derechos de uso: Reconocimiento (by)
Fuente:
Mediterranean Journal of Mathematics. (issn: 1660-5446 )
DOI: 10.1007/s00009-022-02171-7
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s00009-022-02171-7
Código del Proyecto:
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/
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/
info:eu-repo/grantAgreement/NSFC//12071181/
info:eu-repo/grantAgreement/UJI//UJI-B2019-03/
info:eu-repo/grantAgreement/AEI//PGC2018-096872-B-I00//GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS/
Agradecimientos:
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 ...[+]
Tipo: Artículo

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)

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)

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) [+]
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)

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)

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)

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)

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)

Beltrán, A., Felipe, M.J., Melchor, C.: Squares of real conjugacy classes in finite groups. Ann. Mat. Pura Appl. 197(2), 317–328 (2018)

Camina, R.D.: Applying combinatorial results to products of conjugacy classes. J. Group Theory 23(5), 917–923 (2020)

Guralnick, R.M., Navarro, G.: Squaring a conjugacy class and cosets of normal subgroups. Proc. Am. Math. Soc. 144(5), 1939–1945 (2016)

Huppert, B.: Character Theory of Finite Groups. Walter de Gruyter, Berlin (1998)

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

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