On some classes of sublattices of the subgroup lattice

Authors

Keywords:

group, subgroup lattice, modular lattice, formation Fitting set, Fitting formation

Abstract

In this paper G always denotes a group. If K and H are subgroups of G, where K is a normal subgroup of H, then the factor group of H by K is called a section of G. Such a section is called normal, if K and H are normal subgroups of G, and trivial, if K and H are equal. We call any set S of normal sections of G a stratification of G, if S contains every trivial normal section of G, and we say that a stratification S of G is G-closed, if S contains every such a normal section of G, which is G-isomorphic to some normal section of G belonging S. Now let S be any G-closed stratification of G, and let L be the set of all subgroups A of G such that the factor group of V by W, where V is the normal closure of A in G and W is the normal core of A in G, belongs to S. In this paper we describe the conditions on S under which the set L is a sublattice of the lattice of all subgroups of G and we also discuss some applications of this sublattice in the theory of generalized finite T-groups.

Author Biography

  • Alexander N. Skiba, Francisk Skorina Gomel State University, 104 Saveckaja Street, Homiel 246019, Belarus

    doctor of science (physics and mathematics), full professor; professor at the department of algebra and geometry, faculty of mathematics and technologies of programming

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Published

2019-11-24

Issue

No. 3 (2019): Journal of the Belarusian State University. Mathematics and Informatics

Section

Mathematical Logic, Algebra and Number Theory

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How to Cite

[1]
Skiba, A.N. 2019. On some classes of sublattices of the subgroup lattice. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Nov. 2019), 35–47. DOI:https://doi.org/10.33581/2520-6508-2019-3-35-47.