Keywords: group; diassociative IP loop; Moufang loop; finite embeddability property; local embeddability
@article{10_21136_MB_2021_0065_20,
author = {Ghumashyan, Heghine and Guri\v{c}an, Jaroslav},
title = {Sofic groups are not locally embeddable into finite {Moufang} loops},
journal = {Mathematica Bohemica},
pages = {11--18},
year = {2022},
volume = {147},
number = {1},
doi = {10.21136/MB.2021.0065-20},
mrnumber = {4387465},
zbl = {07547238},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0065-20/}
}
TY - JOUR AU - Ghumashyan, Heghine AU - Guričan, Jaroslav TI - Sofic groups are not locally embeddable into finite Moufang loops JO - Mathematica Bohemica PY - 2022 SP - 11 EP - 18 VL - 147 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0065-20/ DO - 10.21136/MB.2021.0065-20 LA - en ID - 10_21136_MB_2021_0065_20 ER -
%0 Journal Article %A Ghumashyan, Heghine %A Guričan, Jaroslav %T Sofic groups are not locally embeddable into finite Moufang loops %J Mathematica Bohemica %D 2022 %P 11-18 %V 147 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/MB.2021.0065-20/ %R 10.21136/MB.2021.0065-20 %G en %F 10_21136_MB_2021_0065_20
Ghumashyan, Heghine; Guričan, Jaroslav. Sofic groups are not locally embeddable into finite Moufang loops. Mathematica Bohemica, Tome 147 (2022) no. 1, pp. 11-18. doi: 10.21136/MB.2021.0065-20
[1] Baumslag, G., Solitar, D.: Some two-generator one-relator non-Hopfian groups. Bull. Am. Math. Soc. 68 (1962), 199-201. | DOI | MR | JFM
[2] Ceccherini-Silberstein, T., Coornaert, M.: Cellular Automata and Groups. Springer Monographs in Mathematics. Springer, Berlin (2010). | DOI | MR | JFM
[3] Collins, B., Dykema, K. J.: Free products of sofic groups with amalgamation over monotileably amenable groups. Münster J. Math. 4 (2011), 101-118. | MR | JFM
[4] Drápal, A.: A simplified proof of Moufang's theorem. Proc. Am. Math. Soc. 139 (2011), 93-98. | DOI | MR | JFM
[5] Glebsky, L. Y., Gordon, Y. I.: On approximation of amenable groups by finite quasigroups. J. Math. Sci. 140 (2007), 369-375. | DOI | MR | JFM
[6] Henkin, L.: Two concepts from the theory of models. J. Symb. Log. 21 (1956), 28-32. | DOI | MR | JFM
[7] Higman, G., Neumann, B. H., Neumann, H.: Embedding theorems for groups. J. Lond. Math. Soc. 24 (1949), 247-254. | DOI | MR | JFM
[8] Lyndon, R. C., Schupp, P. E.: Combinatorial Group Theory. Classics in Mathematics. Springer, Berlin (2001). | DOI | MR | JFM
[9] Magnus, W., Karrass, A., Solitar, D.: Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations. Dover Books on Mathematics. Dover Publications, Mineola (2004). | MR | JFM
[10] Mal'tsev, A. I.: On a general method for obtaining local theorems in group theory. Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Fak. 1 (1941), 3-9 Russian. | MR
[11] Mal'tsev, A. I.: On homomorphisms onto finite groups. Twelve Papers in Algebra American Mathematical Society Translations: Series 2, 119. American Mathematical Society (1983), 67-79. | DOI | JFM
[12] Meskin, S.: Nonresidually finite one-relator groups. Trans. Am. Math. Soc. 164 (1972), 105-114. | DOI | MR | JFM
[13] Pflugfelder, H. O.: Quasigroups and Loops: Introduction. Sigma Series in Pure Mathematics 7. Heldermann Verlag, Berlin (1990). | MR | JFM
[14] Vershik, A. M., Gordon, E. I.: Groups that are locally embeddable in the class of finite groups. St. Petersbg. Math. J. 9 (1998), 49-67. | MR | JFM
[15] Vodička, M., Zlatoš, P.: The finite embeddability property for IP loops and local embeddability of groups into finite IP loops. Ars Math. Contemp. 17 (2019), 535-554. | DOI | MR | JFM
[16] Weiss, B.: Monotileable amenable groups. Topology, Ergodic Theory, Real Algebraic Geometry: Rokhlin's Memorial American Mathematical Society Translations: Series 2, 202. American Mathematical Society (2001), 257-262. | DOI | MR | JFM
[17] Ziman, M.: Extensions of Latin subsquares and local embeddability of groups and group algebras. Quasigroups Relat. Syst. 11 (2004), 115-125. | MR | JFM
Cité par Sources :