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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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dc.contributor.author Beltrán, Antonio es_ES
dc.contributor.author Felipe Román, María Josefa es_ES
dc.contributor.author Shao, Changguo es_ES
dc.date.accessioned 2016-05-19T10:10:08Z
dc.date.available 2016-05-19T10:10:08Z
dc.date.issued 2015-10
dc.identifier.issn 0373-3114
dc.identifier.uri http://hdl.handle.net/10251/64385
dc.description.abstract 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 of a finite group GG and let pp be a fixed prime. Suppose that |xG|=1|xG|=1 or mm for every qq-element of NN and for every prime q≠pq≠p. Then, NN has nilpotent pp-complements. es_ES
dc.description.sponsorship 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 express his deep gratitude for the warm hospitality he has received in the Departamento de Matematicas of the Universidad Jaume I in Castellon, Spain. This research is supported by the Valencian Government, Proyecto PROMETEO/2011/30, by the Spanish Government, Proyecto MTM2010-19938-C03-02. The third author is supported by the research Project NNSF of China (Grant Nos. 11201401 and 11301218) and University of Jinan Research Funds for Doctors (XBS1335 and XBS1336). en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Annali di Matematica Pura ed Applicata 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 Normal subgroups es_ES
dc.subject Prime-power order element es_ES
dc.subject p′p′-Elements es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Class sizes of prime-power order p'-elements and normal subgroups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10231-014-0432-4
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2011%2F030/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJN//XBS1335/ es_ES
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/NSFC//11201401/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11301218/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJN//XBS1336/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation 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 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s10231-014-0432-4 es_ES
dc.description.upvformatpinicio 1527 es_ES
dc.description.upvformatpfin 1533 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 194 es_ES
dc.description.issue 5 es_ES
dc.relation.senia 303968 es_ES
dc.identifier.eissn 1618-1891
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder University of Jinan es_ES
dc.contributor.funder National Natural Science Foundation of China es_ES
dc.contributor.funder Generalitat Valenciana es_ES
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