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Russian Mathematical Surveys, 1972, Volume 27, Issue 6, Pages 149–191
DOI: https://doi.org/10.1070/RM1972v027n06ABEH001394
(Mi rm5141)
 

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
References:
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].
Bibliographic databases:
Document Type: Article
UDC: 519.4
MSC: 22A26, 20E15, 20D30
Language: English
Original paper language: Russian
Citation: M. N. Arshinov, L. E. Sadovskii, “Some lattice-theoretical properties of groups and semi-groups”, Russian Math. Surveys, 27:6 (1972), 149–191
Citation in format AMSBIB
\Bibitem{ArsSad72}
\by M.~N.~Arshinov, L.~E.~Sadovskii
\paper Some lattice-theoretical properties of groups and semi-groups
\jour Russian Math. Surveys
\yr 1972
\vol 27
\issue 6
\pages 149--191
\mathnet{http://mi.mathnet.ru//eng/rm5141}
\crossref{https://doi.org/10.1070/RM1972v027n06ABEH001394}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=404400}
\zmath{https://zbmath.org/?q=an:0278.20030}
Linking options:
  • https://www.mathnet.ru/eng/rm5141
  • https://doi.org/10.1070/RM1972v027n06ABEH001394
  • https://www.mathnet.ru/eng/rm/v27/i6/p139
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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