Characterization of the soluble one-generated totally saturated formations of finite groups

被引：4

作者：

Safonov, V. G. ^{[1
]}

机构：

[1] Gomel State Univ, Gomel, BELARUS

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2007年 / 48卷 / 01期

关键词：

formation of finite groups; totally saturated formation; lattice of formations; tau-closed formation; one-generated formation;

D O I：

10.1007/s11202-007-0015-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the finite length condition for the lattice of tau-closed totally saturated sub-formations of a tau-closed totally saturated formation is equivalent to the finite length condition for this lattice, and it is also equivalent for the formation to be soluble and one-generated.

引用

页码：150 / 155

页数：6

共 50 条

[1] Characterization of the soluble one-generated totally saturated formations of finite groups
V. G. Safonov
Siberian Mathematical Journal, 2007, 48 : 150 - 155
[2] Factorization of One-Generated Formations
A. B. Elovikov
Mathematical Notes, 2003, 73 : 643 - 655
[3] Factorization of one-generated formations
Elovikov, AB
MATHEMATICAL NOTES, 2003, 73 (5-6) : 643 - 655
[4] ON FACTORIZATIONS OF SUBFORMATIONS OF ONE-GENERATED SATURATED FINITE VARIETIES
Vorob'ev, N. N.
COMMUNICATIONS IN ALGEBRA, 2013, 41 (03) : 1087 - 1093
[5] On factorizations of subformations of one-generated hereditary omega-saturated formations
Sel'kin, V. M.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (02): : 232 - 237
[6] On a question of the theory of totally saturated formations of finite groups
Safonov, Vasily G.
ALGEBRA COLLOQUIUM, 2008, 15 (01) : 119 - 128
[7] On modularity of the lattice of totally saturated formations of finite groups
Safonov, Vasily G.
COMMUNICATIONS IN ALGEBRA, 2007, 35 (11) : 3495 - 3502
[8] Factorizations of one-generated composition formations
Wenbin G.
Skiba A.N.
Algebra and Logic, 2001, 40 (5) : 306 - 314
[9] The factorisation of one-generated partially foliated formations
Elovikov, A. B.
DISCRETE MATHEMATICS AND APPLICATIONS, 2009, 19 (04): : 411 - 430
[10] ALGEBRAICITY OF LATTICE OF τ-CLOSED TOTALLY ω-SATURATED FORMATIONS OF FINITE GROUPS
Shcherbina, V. V.
UFA MATHEMATICAL JOURNAL, 2020, 12 (01): : 82 - 90

← 1 2 3 4 5 →