On some classes of sublattices of the subgroup lattice

DOI: https://doi.org/10.33581/2520-6508-2019-3-35-47

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
Keywords: group, subgroup lattice, modular lattice, formation Fitting set, Fitting formation
How to Cite
Skiba, A. N. (2019). On some classes of sublattices of the subgroup lattice. Journal of the Belarusian State University. Mathematics and Informatics, 3, 35-47. https://doi.org/10.33581/2520-6508-2019-3-35-47
Issue
No 3 (2019): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

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