Some lattice-theoretical properties of groups and semi-groups
M. N. Arshinov, L. E. Sadovskii
During the period following the publication of the survey  a number of new papers appeared in which connections between the structure of an algebraic system (a group, a semigroup or a topological group) and the lattice of its subsystems (subgroups, subsemigroups, closed subgroups) are studied.
In a sense the present article is a continuation of , although its style differs somewhat in that it includes fragments of proofs of the most interesting facts.
It also considers other lattices similar to the subgroup lattice of a discrete group. Accordingly it contains five sections studying the subgroup lattice of infinite groups (§ 1), the subsemigroup lattice of these groups (§ 2), the subsemigroup lattice of a semigroup (§ 3), the subgroup lattice in groups with various finiteness conditions (§ 4), and finally the lattice of closed subgroups of a topological group (§ 5).
All the definitions necessary for an understanding of the new results are given here. Definitions of other concepts that are already known well-enough can be found in  or in Kurosh's book .
The authors have tried to examine all the available relevant literature; this is listed at the end of the article. Titles cited in  are repeated here only when they are directly referred to in the text in connection with new results not mentioned in .
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Russian Mathematical Surveys, 1972, 27:6, 149–191
MSC: 22A26, 20E15, 20D30
M. N. Arshinov, L. E. Sadovskii, “Some lattice-theoretical properties of groups and semi-groups”, Uspekhi Mat. Nauk, 27:6(168) (1972), 139–180; Russian Math. Surveys, 27:6 (1972), 149–191
Citation in format AMSBIB
\by M.~N.~Arshinov, L.~E.~Sadovskii
\paper Some lattice-theoretical properties of groups and semi-groups
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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