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Chapter15Group Theory and Applications

Abelian Group
In Abelian groups, when computing,
With operands there's no refuting:
The expression \(bc\)
Is the same as \(cb\).
Not en route to your job, yet commuting.
Howard SpindelThe Omnificent English Dictionary In Limerick Form

In Chapter 11, we introduced groups as a typical algebraic system. The associated concepts of subgroup, group isomorphism, and direct products of groups were also introduced. Groups were chosen for that chapter because they are among the simplest types of algebraic systems. Despite this simplicity, group theory abounds with interesting applications. In this chapter we will introduce some more important concepts in elementary group theory, and some of their applications.