- -

Finite groups with all minimal subgroups solitary

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Finite groups with all minimal subgroups solitary

Show simple item record

Files in this item

dc.contributor.author Esteban Romero, Ramón es_ES
dc.contributor.author Liriano, Orieta es_ES
dc.date.accessioned 2017-06-29T11:47:55Z
dc.date.available 2017-06-29T11:47:55Z
dc.date.issued 2016-10
dc.identifier.issn 0219-4988
dc.identifier.uri http://hdl.handle.net/10251/84110
dc.description.abstract We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. The following result of Gasch¨utz and Itˆo (see [5, Kapitel IV, Satz 5.7; 9]) gives interesting properties of groups with all minimal subgroups normal. es_ES
dc.description.sponsorship The first author has been supported by the research grant MTM2014-54707-C03-1-P from the Ministerio de Economia y Competitividad, Spain and FEDER, European Union. The research of the second author has been done during some visits to the Departament de Matematica Aplicada and the Institut de Matematica Pura i Aplicada of the Universitat Politecnica de Valencia and the Departament d' Algebra of the Universitat de Valencia. She expresses her gratitude to these institutions for the use of their facilities and, especially to the first university for the financial support of some of the visits. en_EN
dc.language Inglés es_ES
dc.publisher World Scientific Publishing es_ES
dc.relation info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/ es_ES
dc.relation Universitat Politècnica de València/ Departament de Matematica Aplicada and the Institut Universitari de Matematica Pura i Aplicada es_ES
dc.relation Universitat de València/ Departament d'Algebra es_ES
dc.relation.ispartof Journal of Algebra and Its Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Finite group es_ES
dc.subject Solitary subgroup es_ES
dc.subject Minimal subgroup es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Finite groups with all minimal subgroups solitary es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1142/S0219498816501401
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escola Tècnica Superior d'Enginyeria Informàtica 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 Esteban Romero, R.; Liriano, O. (2016). Finite groups with all minimal subgroups solitary. Journal of Algebra and Its Applications. 15(8):1650140-1-1650140-9. https://doi.org/10.1142/S0219498816501401 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1142/S0219498816501401 es_ES
dc.description.upvformatpinicio 1650140-1 es_ES
dc.description.upvformatpfin 1650140-9 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 15 es_ES
dc.description.issue 8 es_ES
dc.relation.senia 292702 es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES


This item appears in the following Collection(s)

Show simple item record