Geodesic
Spherically ordered groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1337-1346 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce and study the class of spherically ordered groups. Axioms of spherical orders used for these groups are examined and their (in)dependence is shown. The notions of spherically orderable groups and their spectra of spherical orderability are defined. Values of these spectra are found for a series of certain groups.
Keywords: spherical order, spectrum of spherical orderability.
Mots-clés : group 
@article{SEMR_2024_21_2_a12,
     author = {S. V. Sudoplatov},
     title = {Spherically ordered groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1337--1346},
     year = {2024},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a12/}
}
TY  - JOUR
AU  - S. V. Sudoplatov
TI  - Spherically ordered groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 1337
EP  - 1346
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a12/
LA  - en
ID  - SEMR_2024_21_2_a12
ER  - 
%0 Journal Article
%A S. V. Sudoplatov
%T Spherically ordered groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 1337-1346
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a12/
%G en
%F SEMR_2024_21_2_a12
S. V. Sudoplatov. Spherically ordered groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1337-1346. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a12/

[1] L. Fuchs, Partially ordered algebraic systems, Dover books on mathematics, International series of monographs in pure and applied mathematics, Courier Corporation, 2011 https://books.google.ru/books/about/Partially_Ordered_Algebraic_Systems.html?id=V_k79sVPcqYC&redir_esc=y | Zbl

[2] A.I. Kokorin, V.M. Kopytov, Fully ordered groups, John Wiley Sons, New York-Toronto, 1974 https://books.google.ru/books/about/Fully_Ordered_Groups.html?id=7t2AAAAAIAAJamp;redir_esc=y | MR

[3] V.M. Kopytov, N.Ya. Medvedev, The theory of lattice-ordered groups, Kluwer Academic Publishers, Dordrecht, 1994 | DOI | Zbl

[4] J.A.H. Shepperd, “Transitivities of betweenness and separation and the definitions of betweenness and separation groups”, J. Lond. Math. Soc., s1-31:2 (1956), 240–248 | DOI | Zbl

[5] J.A.H. Shepperd, “Betweenness groups”, J. Lond. Math. Soc., s1-32:3 (1957), 277–285 | DOI

[6] J.A.H. Shepperd, “Separation groups”, Proc. Lond. Math. Soc., III. Ser., 7:1 (1957), 518–548 | DOI | Zbl

[7] J. Gilder, “Betweenness and order in semigroups”, Proc. Camb. Philos. Soc., 61:1 (1965), 13–28 | DOI | Zbl

[8] V.V. Bludov, A.I. Kokorin, “$T$-generically ordred groups”, Sib. Math. J., 20 (1980), 868–872 | DOI | Zbl

[9] Yu.L. Ershov, E.A. Palyutin, Mathematical logic, Fizmatlit, M., 2011 https://www.fml.ru/book/showbook/1384 | Zbl

[10] B.Sh. Kulpeshov, H.D. Macpherson, “Minimality conditions on circularly ordered structures”, Math. Log. Q., 51:4 (2005), 377–399 | DOI | Zbl

[11] S.V. Sudoplatov, “Arities and aritizabilities of first-order theories”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 889–901 http://semr.math.nsc.ru/v19/n2/p889-901.pdf | Zbl

[12] B.Sh. Kulpeshov, S.V. Sudoplatov, “Spherical orders, properties and countable spectra of their theories”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 588–599 http://semr.math.nsc.ru/v20/n2/p588-599.pdf | Zbl

[13] S.V. Sudoplatov, “Minimality conditions, topologies, and ranks for spherically ordered theories”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 600–615 http://semr.math.nsc.ru/v20/n2/p600-615.pdf | Zbl

[14] P.S. Aleksandrov, Combinatorial topology, OGIZ, M.–L., 1947 http://e-heritage.ru/Book/10079077 | Zbl

[15] M. Hachimori, Orientations on simplicial complexes and cubical complexes, Preprint, University of Tsukuba, 2006 https://www.sk.tsukuba.ac.jp/h̃achi/archives/cubic_morse4.pdf

[16] P.S. Modenov, A.S. Parkhomenko, Geometric transformations, Izdat. Mosk. Univ., Moscow, 1961 https://www.mathedu.ru/text/modenov_parhomenko_geometricheskie_preobrazovaniya_1961/p0/ | Zbl

[17] K. Muliarchyk, Free products of bi-orderable groups, 2024, arXiv: 2403.14779 | DOI