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)



Some nonprojective subgroups of free topological groups

Author: Ronald Brown
Journal: Proc. Amer. Math. Soc. 52 (1975), 433-440
MSC: Primary 22A05
MathSciNet review: 0393326
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For the free topological group on an interval $ [a,b]$ a family of closed, locally path-connected subgroups is given such that each group is not projective and so not free topological. Simplicial methods are used, and the test for nonprojectivity is nonfreeness of the group of path components. Similar results are given for the abelian case.

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

  • [1] R. Brown and J. P. L. Hardy, Subgroups of free topological groups and free products of topological groups, J. London Math. Soc. (2) 10 (1975). MR 0382535 (52:3418)
  • [2] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [3] P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag, New York, 1967. MR 35 #1019. MR 0210125 (35:1019)
  • [4] M. I. Graev, Free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-324; English transl., Amer. Math. Soc. Transl. (1) 8 (1962), 305-364. MR 10, 11. MR 0025474 (10:11d)
  • [5] C. E. Hall, $ \mathcal{J}$-projective objects, Proc. Amer. Math. Soc. 26 (1970), 193-195. MR 41 #3555. MR 0258910 (41:3555)
  • [6] J. P. May, Simplicial objects in algebraic topology, Van Nostrand Math. Studies, no. 11, Van Nostrand, Princeton, N. J., 1967. MR 36 #5942. MR 0222892 (36:5942)
  • [7] S. A. Morris, Remarks on varieties of topological groups, Mat. Časopis Sloven. Akad. Vied. 24 (1974), 7. MR 0460518 (57:511)
  • [8] A. S. Morris, E. T. Ordman and H. B. Thompson, The topology of free products of topological groups, Second Internat. Conf. on Group Theory (Canberra, 1973), Lecture Notes in Math., vol. 372, Springer, Berlin and New York, 1974, pp. 504-515. MR 0360912 (50:13359)
  • [9] P. Nickolas, Subgroups of the free topological group on $ [0,1]$, J. London Math. Soc. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22A05

Retrieve articles in all journals with MSC: 22A05

Additional Information

Keywords: Free topological group, projective topological group
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society