On free products of finite abelian groups
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- by Michael Anshel and Robert Prener PDF
- Proc. Amer. Math. Soc. 34 (1972), 343-345 Request permission
Abstract:
The purpose of this note is to show that if G is the free product of finitely many, finite abelian groups then the commutator subgroup is a finitely generated free group whose rank depends only on the number and orders of the factors. Moreover, we shall present a constructive procedure for obtaining a basis of this free group using the Kurosh rewriting process.References
- 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
- P. J. Higgins, Presentations of groupoids, with applications to groups, Proc. Cambridge Philos. Soc. 60 (1964), 7–20. MR 158018, DOI 10.1017/s0305004100037397 Robert A. Prener, The lower central series of special groups generated by elements of order two, Ph.D. Thesis, Polytechnic Institute of Brooklyn.
- Hermann V. Waldinger, The lower central series of groups of a special class, J. Algebra 14 (1970), 229–244. MR 260882, DOI 10.1016/0021-8693(70)90124-9
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 343-345
- MSC: Primary 20E30
- DOI: https://doi.org/10.1090/S0002-9939-1972-0302768-4
- MathSciNet review: 0302768