Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the equivalence of three local theorem techniques


Authors: K. K. Hickin and J. M. Plotkin
Journal: Proc. Amer. Math. Soc. 35 (1972), 389-392
MSC: Primary 20E25
DOI: https://doi.org/10.1090/S0002-9939-1972-0302765-9
MathSciNet review: 0302765
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A result formulated by P. Hall which is used in obtaining local theorems in group theory is shown to be equivalent to the projection set theorem of Kuroš and to the existence of Malcev vectors for local systems.


References [Enhancements On Off] (What's this?)

  • [1] J. D. Halpern and A. Lévy, The Boolean prime ideal theorem does not imply the axiom of choice., Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 83–134. MR 0284328
  • [2] A. G. Kurosh, The theory of groups, Chelsea Publishing Co., New York, 1960. Translated from the Russian and edited by K. A. Hirsch. 2nd English ed. 2 volumes. MR 0109842
  • [3] A. Mal′cev, On a general method for obtaining local theorems in group theory, Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Fak. 1 (1941), no. 1, 3–9 (Russian). MR 0075939
  • [4] D. H. McLain, Local theorems in universal algebras, J. London Math. Soc. 34 (1959), 177–184. MR 0104608, https://doi.org/10.1112/jlms/s1-34.2.177
  • [5] Abraham Robinson, On the construction of models, Essays on the foundations of mathematics, Magnes Press, Hebrew Univ., Jerusalem, 1961, pp. 207–217. MR 0162719
  • [6] Derek J. S. Robinson, Infinite soluble and nilpotent groups, Queen Mary College Mathematics Notes, Queen Mary College, London, 1967. MR 0269740

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E25

Retrieve articles in all journals with MSC: 20E25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0302765-9
Keywords: Local system, inverse limit system, Malcev vector, Boolean prime ideal theorem
Article copyright: © Copyright 1972 American Mathematical Society