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Chapter 7 Groups

We have already met two families of algebraic structures with a single operation: the additive group underlying every ring, and the multiplicative group of units of a field. In this chapter we isolate that common structure, the group, and develop its basic theory: subgroups, homomorphisms, normal subgroups, and quotient groups. This machinery is what makes group actions and the Sylow theorems possible.

This chapter was written by Claude, Anthropic’s AI model, from an outline of topics specified by the course instructor, adapting material from Thomas W. Judson’s original text.

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