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Thompson-like characterization of solubility for products of finite groups

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Thompson-like characterization of solubility for products of finite groups

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Hauck, P.; Kazarin, LS.; Martínez-Pastor, A.; Pérez-Ramos, MD. (2021). Thompson-like characterization of solubility for products of finite groups. Annali di Matematica Pura ed Applicata (1923 -). 200(1):337-362. https://doi.org/10.1007/s10231-020-00998-z

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Título: Thompson-like characterization of solubility for products of finite groups
Autor: Hauck, P. Kazarin, L. S. Martínez-Pastor, Ana Pérez-Ramos, M. D.
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
Fecha difusión:
Resumen:
[EN] A remarkable result of Thompson states that a finite group is soluble if and only if all its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area ...[+]
Palabras clave: Solubility , Products of subgroups , Two-generated subgroups , S-connection , Almost simple groups , Independent primes
Derechos de uso: Reserva de todos los derechos
Fuente:
Annali di Matematica Pura ed Applicata (1923 -). (issn: 0373-3114 )
DOI: 10.1007/s10231-020-00998-z
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s10231-020-00998-z
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/P.G. Demidov Yaroslavl State University//VIP-008/
info:eu-repo/grantAgreement/Generalitat Valenciana//Prometeo%2F2017%2F057//Grupos y semigrupos: estructura y aplicaciones/
Agradecimientos:
Research supported by Proyectos PROMETEO/2017/057 from the Generalitat Valenciana (Valencian Community, Spain) and PGC2018-096872-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades, Spain, and FEDER, European ...[+]
Tipo: Artículo

References

Abe, S., Iiyori, N.: A generalization of prime graphs of finite groups. Hokkaido Math. J. 29, 391–407 (2000)

Amberg, B., Carocca, A., Kazarin, L.: Criteria for the solubility and non-simplicity of finite groups. J. Algebra 285, 58–72 (2005)

Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Clarendon Press, Oxford (1992) [+]
Abe, S., Iiyori, N.: A generalization of prime graphs of finite groups. Hokkaido Math. J. 29, 391–407 (2000)

Amberg, B., Carocca, A., Kazarin, L.: Criteria for the solubility and non-simplicity of finite groups. J. Algebra 285, 58–72 (2005)

Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Clarendon Press, Oxford (1992)

Amberg, B., Kazarin, L.: On the soluble graph of a finite simple group. Commun. Algebra 41, 2297–2309 (2013)

Asaad, M., Shaalan, A.: On the supersolvability of finite groups. Arch. Math. 53, 318–326 (1989)

Baer, R.: Supersoluble immersion. Can. J. Math. 11, 353–369 (1959)

Ballester-Bolinches, A., Ezquerro, L.M.: Classes of Finite Groups. Springer, Berlin (2006)

Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: On finite soluble products of ${\cal{N}}$-connected groups. J. Group Theory 2, 291–299 (1999)

Beidleman, J., Heineken, H.: Pairwise ${\cal{N}}$-connected products of certain classes of finite groups. Commun. Algebra 32, 4741–4752 (2004)

Bray, J.N., Holt, D.F., Roney-Dougal, C.M.: The Maximal Subgroups of the Low-Dimensional Finite Classical Groups. Cambridge University Press, Cambridge (2013)

Carocca, A.: A note on the product of ${mathcal F }$-subgroups in a finite group. Proc. Edinb. Math. Soc. (2) 39, 37–42 (1996)

Carocca, A.: Solvability of factorized finite groups. Glasgow Math. J. 42, 271–274 (2000)

Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Clarendon Press, Oxford (1985)

Dixon, J.D., Mortimer, B.: Permutation Groups. Springer, Berlin (1996)

Doerk, K., Hawkes, T.: Finite Soluble Groups. Walter de Gruyter, Berlin (1992)

Dolfi, S., Guralnick, R.M., Herzog, M., Praeger, C.E.: A new solvability criterion for finite groups. J. Lond. Math. Soc. 85, 269–281 (2012)

Gállego, M. P., Hauck, P., Kazarin, L. S., Martínez-Pastor, A., Pérez-Ramos, M. D.: Products of finite connected subgroups. Preprint. arXiv:1908.03347

Gállego, M.P., Hauck, P., Pérez-Ramos, M.D.: Soluble products of connected subgroups. Rev. Mat. Iberoam. 24, 433–461 (2008)

Gállego, M.P., Hauck, P., Pérez-Ramos, M.D.: On 2-generated subgroups and products of groups. J. Group Theory 11, 851–867 (2008)

Gállego, M.P., Hauck, P., Pérez-Ramos, M.D.: Saturated formations and products of connected subgroups. J. Algebra 333, 105–119 (2011)

Gállego, M.P., Hauck, P., Pérez-Ramos, M.D.: 2-Engel relations between subgroups. J. Algebra 447, 31–55 (2016)

Gordeev, N., Grunewald, F., Kunyavskiĭ, B., Plotkin, E.: Baer–Suzuki theorem for the solvable radical of a finite group. C. R. Acad. Sci. Paris Sér. I(347), 217–222 (2009)

Gordeev, N., Grunewald, F., Kunyavskiĭ, B., Plotkin, E.: From Thompson to Baer–Suzuki: a sharp characterization of the solvable radical. J. Algebra 323, 2888–2904 (2010)

Guest, S.: A solvable version of the Baer–Suzuki theorem. Trans. Am. Math. Soc. 362, 5909–5946 (2010)

Guest, S., Levy, D.: Criteria for solvable radical membership via $p$-elements. J. Algebra 415, 88–111 (2014)

Guralnick, R., Kunyavskiĭ, B., Plotkin, E., Shalev, A.: Thompson-like characterizations of the solvable radical. J. Algebra 300, 363–375 (2006)

Grunewald, F., Kunyavskiĭ, B., Plotkin, E.: Characterization of solvable groups and solvable radical. Int. J. Algebra Comput. 23, 1011–1062 (2013)

Hauck, P., Martínez-Pastor, A., Pérez-Ramos, M.D.: Products of $\cal{N}$-connected groups. Ill. J. Math. 47, 1033–1045 (2003)

Hering, C., Liebeck, M.W., Saxl, J.: The factorizations of the finite exceptional groups of Lie type. J. Algebra 106, 517–527 (1987)

Huppert, B.: Zweifach transitive, auflösbare Permutationsgruppen. Math. Z. 68, 126–150 (1957)

Huppert, B.: Endliche Gruppen I. Springer, Berlin (1967)

Iiyory, N.: $p$-Solvability and a generalization of prime graphs of finite groups. Commun. Algebra 30, 1679–1691 (2002)

Kleidman, P., Liebeck, M.: The subgroup structure of the finite classical groups. Cambridge University Press, Cambridge (1990)

Liebeck, M.W., Praeger, C.E., Saxl, J.: The maximal factorizations of the finite simple groups and their automorphism groups. Mem. AMS 86, 432 (1990)

Maier, R.: A completeness property of certain formations. Bull. Lond. Math. Soc. 24, 540–544 (1992)

Malle, G., Saxl, J., Weigel, T.: Generation of classical groups. Geom. Dedicata 49, 85–116 (1994)

Ramanujan, S.: A proof of Bertrand’s postulate. J. Indian Math. Soc. 11, 181–182 (1919)

The GAP Group, GAP—Groups, Algorithms, and Programming. http://www.gap-system.org, Version 4.10.2 (2019)

Thompson, J.: Nonsolvable finite groups all of whose local subgroups are solvable. Bull. Am. Math. Soc. 74, 383–437 (1968)

Wiegold, J., Williamson, A.G.: The factorisation of the alternating and symmetric groups. Math. Z. 175, 171–179 (1980)

Zorn, M.: Nilpotency of finite groups. Bull. Am. Math. Soc. 42, 485–486 (1936)

Zsigmondy, K.: Zur Theorie der Potenzreste. Monatsh. Math. Phys. 3, 265–284 (1892)

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