Cycle Notation gives you a way to compactly write down a permutation. Since the symmetric group is so important in the study of groups, learning cycle notation will speed up your work with the group Sn. In this lesson we show you how to convert a permutation into cycle notation, talk about the conventions, and discuss the key properties of cycles.
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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.