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
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/84110
Title:
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Finite groups with all minimal subgroups solitary
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Author:
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Esteban Romero, Ramón
Liriano, Orieta
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UPV Unit:
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Universitat Politècnica de València. Escola Tècnica Superior d'Enginyeria Informàtica
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
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Issued date:
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Abstract:
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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 ...[+]
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.
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Subjects:
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Finite group
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Solitary subgroup
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Minimal subgroup
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Algebra and Its Applications. (issn:
0219-4988
)
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DOI:
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10.1142/S0219498816501401
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Publisher:
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World Scientific Publishing
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Publisher version:
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http://dx.doi.org/10.1142/S0219498816501401
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Project ID:
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info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/
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Thanks:
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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 ...[+]
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.
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Type:
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Artículo
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