18.703 Modern Algebra, Quotient Groups

Abstract

Given a group G and a subgroup H, under what circumstances can we find a homomorphism φ : G −→ G', such that H is the kernel of φ? Clearly a necessary condition is that H is normal in G. Somewhat surprisingly this trivially necessary condition is also in fact sufficient. The idea is as follows. Given G and H there is an obvious map of sets, where H is the… (More)

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