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8.1: Motivation
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We mentioned previously that given a subgroup H of G, we'd like to use H to get at some understanding of G's entire structure. Recall that we've defined G/H to be the set of all left cosets of H in G. What we'd like to do now is equip G/H with some operation under which G/H is a group!
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8.2: Focusing on Normal Subgroups
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In this section, we will define a normal subgroup and provide a theorem that will help us in identifying when a subgroup of a group is normal.
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8.3: Introduction to Factor Groups
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We now return to the notion of equipping G/H, when H⊴G, with a group structure. We have already saw that left coset multiplication on G/H is well-defined when H⊴G (Theorem 8.1.1); it turns out that given this, it is very easy to prove that G/H under this operation is a group.
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8.4: Exercises
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This page contains the exercises for Chapter 8.