ON SUBLATTICES OF THE LATTICE OF PARTIALLY TOTALLY SATURATED FORMATIONS OF FINITE GROUPS

Author(s):  V.V. Shcherbina, Belarusian State University, Minsk, Republic of Belarus, shcherbinavv@tut.by

V.G. Safonov, Dr., Prof., Belarusian State University, Minsk, Republic of Belarus

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  All groups under consideration are finite. The paper studies some properties of the lattice of all  - closed totally -saturated formations. Using methods of V.G. Safonov and L.A. Shemetkov, we prove that for any subgroup functor  , the lattice of all  -closed totally -saturated formations is a complete sublattice of the lattice of all totally -saturated formations. In particular, we show that the lattice of all  -closed totally saturated formations is a complete sublattice of the lattice of all totally saturated formations. Similarly, the lattice of all  -closed totally p -saturated formations is a complete sublattice of the lattice of all totally p -saturated formations.

Keywords:  formation of finite groups, totally  -saturated formation, lattice of formations,  -closed formation

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