Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order, alternating groups An (n bigger than 4), groups of Lie type, and the 26 sporadic groups, including the Monster Group.
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Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.