The abelianization of almost free groups
HTML articles powered by AMS MathViewer
- by Charly Bitton PDF
- Proc. Amer. Math. Soc. 129 (2001), 1799-1803 Request permission
Abstract:
We will construct an almost free non-free group $G$ of cardinality $\aleph _{1}$ such that $G/G’$ is a free abelian group.References
- C. Bitton, Problems in set theory arising from group theory, PhD thesis, The Hebrew University, 1998.
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Menachem Magidor and Saharon Shelah, When does almost free imply free? (For groups, transversals, etc.), J. Amer. Math. Soc. 7 (1994), no. 4, 769–830. MR 1249391, DOI 10.1090/S0894-0347-1994-1249391-8
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
- Saharon Shelah, A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math. 21 (1975), no. 4, 319–349. MR 389579, DOI 10.1007/BF02757993
- Saharon Shelah, Incompactness in regular cardinals, Notre Dame J. Formal Logic 26 (1985), no. 3, 195–228. MR 796637, DOI 10.1305/ndjfl/1093870869
Additional Information
- Charly Bitton
- Affiliation: Institute of Mathematics, Hebrew University, Jerusalem, Israel
- Address at time of publication: Department of Mathematics, University of California, Irvine, California 92679
- Email: cbitton@math.uci.edu
- Received by editor(s): May 5, 1999
- Received by editor(s) in revised form: October 5, 1999
- Published electronically: November 21, 2000
- Additional Notes: This is part of the author’s Ph.D. thesis done under the supervision of Professor M. Magidor to whom the author is greatly indebted for his help.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1799-1803
- MSC (1991): Primary 03E75, 03E05, 20K27
- DOI: https://doi.org/10.1090/S0002-9939-00-05730-0
- MathSciNet review: 1814113