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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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dc.contributor.author Alemany Martínez, Elena es_ES
dc.contributor.author Beltrán, Antonio es_ES
dc.contributor.author Felipe Román, María Josefa
dc.date.accessioned 2013-09-09T12:05:06Z
dc.date.issued 2012
dc.identifier.issn 0004-9727
dc.identifier.uri http://hdl.handle.net/10251/31896
dc.description.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 p-complement or G = PQ x A, with P and Q a Sylow p-subgroup and a Sylow q-subgroup of G, respectively, and A is abelian. In particular, we provide a new extension of Ito's theorem on groups having exactly two class sizes for elements of prime power order. es_ES
dc.description.sponsorship 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 by grant Fundacio Caixa-Castello P11B2010-47. en_EN
dc.language Inglés es_ES
dc.publisher Cambridge University Press es_ES
dc.relation.ispartof Bulletin of the Australian Mathematical Society es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Finite groups es_ES
dc.subject Conjugacy class sizes es_ES
dc.subject Solvable groups es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Itô's theorem on groups with two class sizes revisited es_ES
dc.type Artículo es_ES
dc.embargo.lift 10000-01-01
dc.embargo.terms forever es_ES
dc.identifier.doi 10.1017/S0004972711002875
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-19938-C03-02/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. III/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2011%2F030/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJI//P1·1B2010-47/ es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada es_ES
dc.description.bibliographicCitation 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 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1017/S0004972711002875 es_ES
dc.description.upvformatpinicio 476 es_ES
dc.description.upvformatpfin 481 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 85 es_ES
dc.relation.senia 239237
dc.identifier.eissn 1755-1633
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Universitat Jaume I; Fundació Caixa Castelló - Bancaixa es_ES
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dc.description.references 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 es_ES
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dc.description.references Shirong, L. (1996). Finite groups with exactly two class lengths of elements of prime power order. Archiv der Mathematik, 67(2), 100-105. doi:10.1007/bf01268923 es_ES
dc.description.references Itô, N. (1953). On Finite Groups with Given Conjugate Types I. Nagoya Mathematical Journal, 6, 17-28. doi:10.1017/s0027763000016937 es_ES
dc.description.references Camina, R. D., & Camina, A. R. (1998). Implications of conjugacy class size. Journal of Group Theory, 1(3). doi:10.1515/jgth.1998.017 es_ES
dc.description.references 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 es_ES


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