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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 completedoi:10.14288/1.0080558 fatcat:zicjqiykszds7c4dmoltdvjpie