Text complete end PDF
Services on Demand
Journal
Article
Indicators
- Cited by SciELO
- Access statistics
Related links
- Cited by Google
- Similars in SciELO
- Similars in Google
Share
Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.52 no.2 Bogotá Jul./Dec. 2018
https://doi.org/10.15446/recolma.v52n2.77156
Original articles
Inductive lattices of totally composition formations
Retículos inductivos de formaciones totalmente compositivas
1 Jeju National University, Jeju, Korea
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
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
References
[1] J. A. Cabrera and I. Gutiérrez-García, Sobre clases de grupos finitos solubles, Matemáticas: Enseñanza Universitaria XII (2004), no. 2, 53-68, (in Spanish). [ Links ]
[2] K. Doerk and T. Hawkes, Finite soluble groups, De Gruyter Expositions in Mathematics, 4, Walter de Gruyter, Berlin, New York, 1992. [ Links ]
[3] W. Gaschütz, Zur theorie der endlichen auflösbaren gruppen, Mathematische Zeitschrift 80 (1963), no. 4, 300-305. [ Links ]
[4] W. Guo, Structure theory for canonical classes of finite groups, SpringerVerlag Berlin Heidelberg, 2015, 359 p. [ Links ]
[5] W. Guo and A. N. Skiba, Two remarks on the identities of lattices of ω-local and ω-composition formations of finite groups, Russian Math. 46 (2002), no. 5, 12-20. [ Links ]
[6] V. G. Safonov, On the modularity of the lattice of τ-closed totally saturated formations of finite groups, Ukrainian Math. Journal 58 (2006), no. 6, 967-973. [ Links ]
[7] ______, On a question of the theory of totally saturated formations of finite groups, Algebra Colloq. 15 (2008), no. 1, 119-128. [ Links ]
[8] ______, On modularity of the lattice of totally saturated formations of finite groups, Comm. Algebra 35 (2011), no. 11, 3495-3502. [ Links ]
[9] L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems. Sovremennaya Algebra, Nauka, Moscow, 256 p. (in Russian), 1989. [ Links ]
[10] A. N. Skiba , Algebra of formations, Belaruskaya Navuka, Minsk, 240 p. (in Russian), 1997. [ Links ]
[11] A. N. Skiba and L. A. Shemetkov , Multiply L-composition formations of finite groups, Ukrainian Math. Journal 52 (2000), no. 6, 898-913. [ Links ]
[12] A. Tsarev, Laws of the lattices of foliated formations of T-groups, Rend. Circ. Mat. Palermo, II. Ser., to appear. DOI: 10.1007/s12215-018-0369-3, 2018. [ Links ]
[13] A. Tsarev, On the maximal subformations of partially composition formations of finite groups, Bol. Soc. Mat. Mex., to appear. DOI: 10.1007/s40590-018-0205-y, 2018. [ Links ]
[14] A. Tsarev and N. N. Vorob'ev, Lattices of composition formations of finite groups and the laws, J. Algebra Appl. 17 (2018), no. 5, 1850084 (17 pages). [ Links ]
[15] A. Tsarev , T. Wu, and A. Lopatin, On the lattices of multiply composition formations of finite groups, Bull. Int. Math. Virt. Institute (former Bull. Soc. Math. Banja Luka) 6 (2016), 219-226. [ Links ]
[16] A. A. Tsarev and N. N. Vorob'ev , On a question of the theory of partially composition formations, Algebra Colloq. 21 (2014), no. 3, 437-447. [ Links ]
[17] N. N. Vorob'ev, On one question of the theory of local classes of finite groups, Problems in Algebra. Proc. F. Scorina Gomel State Univ. 14 (1999), 132-140. [ Links ]
[18] N. N. Vorob'ev , On complete sublattices of formations of finite groups, Russian Math. 46 (2002), no. 5, 12-20. [ Links ]
[19] N. N. Vorob'ev , Algebra of Classes of Finite Groups, P. M. Masherov Vitebsk State University, Vitebsk, 322 p. (in Russian), 2012. [ Links ]
[20] N. N. Vorob'ev and A. N. Skiba , On the distributivity of the lattice of solvable totally local Fitting classes, Math. Notes 67 (2000), no. 5, 563-571. [ Links ]
[21] N. N. Vorob'ev , A. N. Skiba , and A. A. Tsarev , Laws of the lattices of partially composition formations, Siberian Math. Journal 62 (2018), no. 1, 17-22. [ Links ]
[22] N. N. Vorob'ev and A. A. Tsarev , On the modularity of a lattice of τclosed n-multiply ω-composition formations, Ukrainian Math. Journal, 62 (2010), no. 4, 453-463. [ Links ]
Received: March 06, 2018; Accepted: May 24, 2018