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This article is cited in 2 scientific papers (total in 2 papers)
Some lattice-theoretical properties of groups and semi-groups
M. N. Arshinov, L. E. Sadovskii
Abstract:
During the period following the publication of the survey [5] 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 [5], 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 [5] or in Kurosh's book [4].
The authors have tried to examine all the available relevant literature; this is listed at the end of the article. Titles cited in [5] are repeated here only when they are directly referred to in the text in connection with new results not mentioned in [5].
Citation:
M. N. Arshinov, L. E. Sadovskii, “Some lattice-theoretical properties of groups and semi-groups”, Russian Math. Surveys, 27:6 (1972), 149–191
Linking options:
https://www.mathnet.ru/eng/rm5141https://doi.org/10.1070/RM1972v027n06ABEH001394 https://www.mathnet.ru/eng/rm/v27/i6/p139
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