Titlebook: Visual Group Theory; A Computer-Oriented Stephan Rosebrock Textbook 20241st edition The Editor(s) (if applicable) and The Author(s), under

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Finite Groups,This chapter is about groups of finite order. In the first section, we present a class of examples of finite groups that will play a role later on.

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Group Operations,owing sections, what we have been doing so far is formalized: We have so far understood a group as a set of isometries of an object. This is clarified and generalized. Groups “operate” or “act” on sets. For example, the group of the plane operates on (the set of points of) the plane.

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Products of Groups,uss three of these possibilities, direct products, free products, and semidirect products, in the following sections. With the help of the semidirect product, we can describe a frieze. At the end, we characterize the possible translation subgroups of symmetry groups in the Euclidean plane.

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