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Class sizes of prime-power order p'-elements and normal subgroups

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Class sizes of prime-power order p'-elements and normal subgroups

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Beltrán, A.; Felipe Román, MJ.; Shao, C. (2015). Class sizes of prime-power order p'-elements and normal subgroups. Annali di Matematica Pura ed Applicata. 194(5):1527-1533. https://doi.org/10.1007/s10231-014-0432-4

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Título: Class sizes of prime-power order p'-elements and normal subgroups
Autor: Beltrán, Antonio Felipe Román, María Josefa Shao, Changguo
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup ...[+]
Palabras clave: Finite groups , Conjugacy class sizes , Normal subgroups , Prime-power order element , p Elements
Derechos de uso: Reserva de todos los derechos
Fuente:
Annali di Matematica Pura ed Applicata. (issn: 0373-3114 ) (eissn: 1618-1891 )
DOI: 10.1007/s10231-014-0432-4
Editorial:
Springer Verlag (Germany)
Versión del editor: http://dx.doi.org/10.1007/s10231-014-0432-4
Código del Proyecto:
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2011%2F030/
...[+]
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2011%2F030/
info:eu-repo/grantAgreement/UJN//XBS1335/
info:eu-repo/grantAgreement/MICINN//MTM2010-19938-C03-02/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. III/
info:eu-repo/grantAgreement/NSFC//11201401/
info:eu-repo/grantAgreement/NSFC//11301218/
info:eu-repo/grantAgreement/UJN//XBS1336/
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Agradecimientos:
We are very grateful to the referee, who provided us a significant simplification of the last step of the proof of the main theorem and for many comments which have contributed to improve the paper. C. G. Shao wants to ...[+]
Tipo: Artículo

References

Akhlaghi, Z., Beltrán, A., Felipe, M.J.: The influence of $$p$$ p -regular class sizes on normal subgroups. J. Group Theory. 16, 585–593 (2013)

Alemany, E., Beltrán, A., Felipe, M.J.: Nilpotency of normal subgroups having two $$G$$ G -class sizes. Proc. Am. Math. Soc. 139, 2663–2669 (2011)

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Akhlaghi, Z., Beltrán, A., Felipe, M.J.: The influence of $$p$$ p -regular class sizes on normal subgroups. J. Group Theory. 16, 585–593 (2013)

Alemany, E., Beltrán, A., Felipe, M.J.: Nilpotency of normal subgroups having two $$G$$ G -class sizes. Proc. Am. Math. Soc. 139, 2663–2669 (2011)

Alemany, E., Beltrán, A., Felipe, M.J.: Finite groups with two $$p$$ p -regular conjugacy class lengths II. Bull. Aust. Math. Soc. 797, 419–425 (2009)

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Huppert, B.: Character Theory of Finite groups, vol. 25. De Gruyter Expositions in Mathemathics, Berlin, New York (1998)

Kleidman, P., Liebeck, M.: The Subgroup Structure of The Finite Classical Groups. London Mathematical Society Lecture Note Series, 129. Cambridge University Press, Cambridge (1990)

Kurzweil, K., Stellmacher, B.: The Theory of Finite Groups. An Introduction. Springer, New York (2004)

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Vasiliev, A.V., Vdovin, E.P.: An adjacency criterion for the prime graph of a finite simple group. Algebra Logic 44(6), 381–406 (2005)

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