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The abelianization of almost free groups

Author(s): Charly Bitton
Journal: Proc. Amer. Math. Soc. 129 (2001), 1799-1803.
MSC (1991): Primary 03E75, 03E05, 20K27
Posted: November 21, 2000
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Abstract:

We will construct an almost free non-free group of cardinality $\aleph_{1}$ such that $G/G^{\prime}$ is a free abelian group.

References:

1.: C. Bitton, Problems in set theory arising from group theory, PhD thesis, The Hebrew University, 1998.
2.: G. Higman, Almost free groups, Proc. London Math. Soc. (3) 1 (1951), 284-290. MR 13:430d
3.: M. Magidor and S. Shelah, When does almost free imply free?, J. Amer. Math. Soc. 7 (1994), 769-830. MR 94m:03081
4.: W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, Dover Publications, New York, 1966. MR 34:7617
5.: S. Shelah, A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math 21 (1975), 319-349. MR 52:10410
6.: S. Shelah, Incompactness in regular cardinals, Notre Dame J. Formal Logic 26 (1985), 195-228. MR 87f:03095

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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

DOI: 10.1090/S0002-9939-00-05730-0
PII: S 0002-9939(00)05730-0
Received by editor(s): May 5, 1999
Received by editor(s) in revised form: October 5, 1999
Posted: 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 of article: Copyright 2000, American Mathematical Society


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