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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.52 no.2 Bogotá jul./dez. 2018

https://doi.org/10.15446/recolma.v52n2.77156 

Original articles

Inductive lattices of totally composition formations

Retículos inductivos de formaciones totalmente compositivas

Aleksandr Tsarev1  * 

1 Jeju National University, Jeju, Korea


Abstract

Let τ be a subgroup functor such that all subgroups of every finite group G contained in τ(G) are subnormal in G. In this paper, we give a simple proof of the fact that the lattice of all τ-closed totally composition formations of finite groups is inductive.

Keywords: Finite group; formation of groups; satellite of formation; τ-closed totally composition formation; inductive lattice of formations

Resumen

Sea τ un funtor de subgrupo de modo que todos los subgrupos de cualquier grupo finito G contenido en τ(G) son subnormales en G. En este artículo, damos una demostración simple de que el retículo de todas las formaciones de composición totalmente τ-cerradas de los grupos finitos es inductivo.

Palabras clave: Grupo finito; formación de grupos; satélite de formación; formación de composición totalmente τ-cerrada; retículo inductivo de formaciones

Text complete end PDF

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Received: March 06, 2018; Accepted: May 24, 2018

* Correspondencia: Aleksandr Tsarev, Department of Mathematics, Jeju National University, Jeju 690-756, Korea. Correo electrónico: alex_vitebsk@mail.ru.

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