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  • Print publication year: 2011
  • Online publication date: July 2011

Engel conditions on orderable groups and in combinatorial problems (a survey)

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Groups St Andrews 2009 in Bath
  • Online ISBN: 9780511842467
  • Book DOI: https://doi.org/10.1017/CBO9780511842467
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References
[1] A., Abdollahi, Finitely generated soluble groups with an Engel condition on infinite subsets, Rend. Sem. Mat. Univ. Padova 103 (2000), 47–49.
[2] A., Abdollahi, Some Engel conditions on infinite subsets of certain groups, Bull. Austral. Math. Soc. 62 (2000), 141–148.
[3] A., Abdollahi, A combinatorial problem in infinite groups, Bull. Malaysian Math. Soc. 25 (2002), 101–114.
[4] A., Abdollahi and B., Taeri, Some conditions on infinite subsets of infinite groups, Bull. Malaysian Math. Soc. 22 (1999), 87–93.
[5] A., Abdollahi and B., Taeri, A condition on finitely generated soluble groups, Comm. Algebra 27 (1999), 5633–5638.
[6] R., Baer, Engelsche Elemente Noetherscher Gruppen, Math. Ann. 133 (1957), 256–270.
[7] Béla, Bollobás, Combinatorics: set, systems, hypergraphs, families of vectors and combinatorial (Cambridge University Press, Cambridge 1986).
[8] V. V., Bludov, A. M. W., Glass and A. H., Rhemtulla, On centrally orderable groups, J. Algebra 291 (2005), 129–143
[9] V. V., Bludov, A. M. W., Glass, V. M., Kopytov and N. Ya., Medvedev, Unsolved Problems in Ordered and Orderable Groups, arXiv:0906.2621v1 [math.GR] (2009).
[10] Roberta Botto, Mura and Akbar H., Rhemtulla, Orderable groups, Lecture Notes in pure and applied mathematics (Marcel Dekker, New York–Basel 1977).
[11] C., Delizia, Finitely generated soluble groups with a condition on infinite subsets, Ist. Lombardo Accad. Sci. Lett. Rend. A 128 (1994), 201–208.
[12] C., Delizia, On groups with a nilpotence condition on infinite subsets, Algebra Colloq. 2 (1995), 97–104.
[13] C., Delizia, On certain residually finite groups, Comm. Algebra 24 (1996), 3531–3535.
[14] C., Delizia, A nilpotency condition for finitely generated soluble groups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 9 (1998), 237–239.
[15] C., Delizia and C., Nicotera, On residually finite groups with an Engel condition on infinite subsets, Houston J. Math. 27 (2001), 757–761.
[16] C., Delizia and C., Nicotera, Groups with conditions on infinite subsets, Ischia Group Theory 2006 (T., Hawkes et al., eds.) (World Scientific Pub Co Inc, Singapore 2007), 46–55.
[17] C., Delizia, A. H., Rhemtulla and H., Smith, Locally graded groups with a nilpotency condition on infinite subsets, J. Austral. Math. Soc. A 69 (2000), 415–420.
[18] G., Endimioni, On a combinatorial problem in varieties of groups, Comm. Algebra 23 (1995), 5297–5307.
[19] Andrew M. W., Glass, Partially ordered groups, World Scientific Series in Algebra 5, (World Scientific Publ. Co. Inc., Singapore 1999).
[20] E. S., Golod, Some problems of Burnside type, Proc. Internat. Congress Math, Moscow, 1966, Izdat. Mir., Moscow (1968), 284–289.
[21] K., Gruenberg, The Engel elements of a soluble group, Illinois J. Math. 3 (1959), 151–168.
[22] G., Havas and M. R., Vaughan-Lee, 4-Engel groups are locally nilpotent, Internat. J. Algebra Comput. 15 (2005), no. 4, 649–682.
[23] O., Hölder, Die Axiome der Quantität and die Lehre vom Mass, Ber. Verh. Sächs. Ges. Wiss. Leipzig, Math. Phys. Cl. 53 (1901), 1–64.
[24] Y., Kim and A. H., Rhemtulla, Weak maximality condition and polycyclic groups, Proc. Amer. Math. Soc. 123 (1995), 711–714.
[25] Y., Kim and A. H., Rhemtulla, Groups with Ordered Structures, Groups–Korea '94 (Pusan) (de Gruyter, Berlin 1995), 199–210.
[26] Y. K., Kim and A. H., Rhemtulla, On locally graded groups, Groups–Korea '94 (Pusan), (de Gruyter, Berlin 1995), 189–197.
[27] Kourovka Notebook, (Ross. Akad. Nauk Sib. Otd., Inst. Mat., Novosibirsk 2002).
[28] J. C., Lennox and J., Wiegold, Extensions of a problem of Paul Erdös on groups, J. Austral. Math. Soc. 31 (1981), 459–463.
[29] P., Longobardi, On locally graded groups with an Engel condition on infinite subsets, Arch. Math. 76 (2001), 88–90.
[30] P., Longobardi and M., Maj, Finitely generated soluble groups with an Engel condition on infinite subsets, Rend. Sem. Mat. Univ. Padova 89 (1993), 97–102.
[31] P., Longobardi and M., Maj, Semigroup identities and Engel groups, Groups St Andrews 1997 in Bath Vol 2 (C. M., Campbell et al., eds.), London Math. Soc. Lecture Note Ser. 261 (CUPCambridge 1999), 527–531.
[32] P., Longobardi and M., Maj, On some classes of orderable groups, Rend. Sem. Mat. Fis. Milano 68 (2001), 203–216.
[33] P., Longobardi, M., Maj and A. H., Rhemtulla, Infinite groups in a given variety and Ramsey's theorem, Comm. Algebra 20 (1992), 127–139.
[34] P., Longobardi, M., Maj, A. H., Rhemtulla, Groups with no free subsemigroups, Trans. Amer. Math. Soc. 347 (1995), 1419–1427.
[35] O., Macedonska, What do the Engel laws and positive laws have in common?, Fundamental and Applied Mathematics (to appear).
[36] J., Milnor, Growth of finitely generated solvable groups, J. Diff. Geom. 2 (1968), 447–449.
[37] B. H., Neumann, A problem of Paul Erdös on groups, J. Austral. Math. Soc. 21 (1976), 467–472.
[38] O., Puglisi and L. S., Spiezia, A combinatorial property of certain infinite groups, Comm. Algebra 22 (1994), 1457–1465.
[39] Derek J. S., Robinson, Finiteness Conditions and Generalized Soluble Groups, Parts I and II, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 62 (Springer-Verlag, New York 1972).
[40] Derek J. S., Robinson, A Course in the Theory of Groups, Second Edition, Graduate Texts Math. 80 (Springer-Verlag, New York 1996).
[41] S., Rosset, A property of groups of non-exponential growth, Proc. Amer. Math. Soc. 54 (1976), 24–26.
[42] L. S., Spiezia, Infinite locally soluble k-Engel groups, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 3 (1992), 177–183.
[43] L. S., Spiezia, A property of the variety of 2-Engel groups, Rend. Sem. Mat. Univ. Padova 91 (1994), 225–228.
[44] L. S., Spiezia, A characterization of third Engel groups, Arch. Math. 64 (1995), 369–373.
[45] D. A., Suprunenko and M. S., Garaščuk, Linear groups with Engel condition, Dokl. Akad. Nauk BSSR 6 (1962), 277–280.
[46] G., Traustason, Semigroup identities in 4-Engel groups, J. Group Theory 2 (1999), 39–46.
[47] G., Traustason, Locally nilpotent 4-Engel groups are Fitting groups, J. Algebra 279 (2003), 7–27.
[48] M. R., Vaughan-Lee and J., Wiegold, Countable locally nilpotent groups of finite exponent with no maximal subgroups, Bull. London Math. Soc. 13 (1981), 45–46.
[49] J. S., Wilson, Two-generator conditions in residually finite groups, Bull. London Math. Soc. 23 (1991), 239–248.
[50] E. I., Zelmanov, On some problems of group theory and Lie algebras, Math. USSRSb 66 (1990), 159–168.
[51] M., Zorn, On a theorem of Engel, Bull. Amer. Math. Soc. 43 (1936), 401–404.
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