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The tensor product of two abelian groups

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Title: The tensor product of two abelian groups
Author: Mitton, David
Degree: Master of Arts - MA
Program: Mathematics
Copyright Date: 1966
Subject Keywords Abelian groups
Issue Date: 2011-08-31
Publisher University of British Columbia
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Abstract: The concept of a free group is discussed first in Chapter 1 and in Chapter 2 the tensor product of two groups for which we write A⊗B is defined by "factoring out" an appropriate subgroup of the free group on the Cartesian product of the two groups. The existence of a unique homomorphism h : A⊗B→H is assured by the existence of a bilinear map f : A×B→H , where H is any group (Lemma 2-2) and this property of the tensor product is used extensively throughout the thesis. In Chapter 3 the complete characterization is given for the tensor product of two arbitrary finitely generated groups. In the last chapter we discuss the structure of A⊗B for arbitrary groups. Essentially, the only complete characterizations are for those cases where one of the two groups is torsion. Many theorems from the theory of Abelian Groups are assumed but some considered interesting are proved herein.
Affiliation: Science, Faculty of
URI: http://hdl.handle.net/2429/37036
Scholarly Level: Graduate

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