Groups and Group Homomorphisms
This chapter introduces the notion of an abstract group, one of the fundamental objects of both algebra and geometry and very much at the heart of linear algebra. In the early stages, the student will perhaps see only a rather arbitrary looking (but attractive!) informal axiomatic system. This is a gross deception. The definition distills millennia of mathematical experience. Another theme also emerges: objects are not nearly so interesting in themselves as the relationships they bear to one another. In the case of groups, these relationships are expressed by group homomorphisms.
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