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Proceedings of the American Mathematical Society

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

 

 

On free products of finite abelian groups


Authors: Michael Anshel and Robert Prener
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0302768-4
Keywords: Finite abelian groups, free products, commutator subgroup, rank, rewriting process
Article copyright: © Copyright 1972 American Mathematical Society