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Itô's theorem on groups with two class sizes revisited

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Itô's theorem on groups with two class sizes revisited

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Alemany Martínez, E.; Beltrán, A.; Felipe Román, MJ. (2012). Itô's theorem on groups with two class sizes revisited. Bulletin of the Australian Mathematical Society. 85:476-481. https://doi.org/10.1017/S0004972711002875

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/31896

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Title: Itô's theorem on groups with two class sizes revisited
Author: Alemany Martínez, Elena Beltrán, Antonio Felipe Román, María Josefa
UPV Unit: 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
Issued date:
Abstract:
Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p(a)q(b), for two distinct primes p and q, and G either has an abelian ...[+]
Subjects: Finite groups , Conjugacy class sizes , Solvable groups
Copyrigths: Cerrado
Source:
Bulletin of the Australian Mathematical Society. (issn: 0004-9727 ) (eissn: 1755-1633 )
DOI: 10.1017/S0004972711002875
Publisher:
Cambridge University Press
Publisher version: http://dx.doi.org/10.1017/S0004972711002875
Project ID:
info:eu-repo/grantAgreement/MICINN//MTM2010-19938-C03-02/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. III/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2011%2F030/
info:eu-repo/grantAgreement/UJI//P1·1B2010-47/
Thanks:
This research is supported by the Spanish Government, Proyecto MTM2010-19938-C03-02 and the second and third authors are supported by the Valencian Government, Proyecto PROMETEO/2011/30. The second author is also supported ...[+]
Type: Artículo

References

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Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433 [+]
Huppert, B. (1998). Character Theory of Finite Groups. doi:10.1515/9783110809237

Baer, R. (1953). Group elements of prime power index. Transactions of the American Mathematical Society, 75(1), 20-20. doi:10.1090/s0002-9947-1953-0055340-0

Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433

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Itô, N. (1953). On Finite Groups with Given Conjugate Types I. Nagoya Mathematical Journal, 6, 17-28. doi:10.1017/s0027763000016937

Camina, R. D., & Camina, A. R. (1998). Implications of conjugacy class size. Journal of Group Theory, 1(3). doi:10.1515/jgth.1998.017

Beltrán, A., & Felipe, M. J. (2004). Prime powers as conjugacy class lengths of π-elements. Bulletin of the Australian Mathematical Society, 69(2), 317-325. doi:10.1017/s0004972700036054

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