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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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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Group Presentations,sentation is called a presentation of a group and describes it completely. Conversely, however, it is generally not possible to decide from two given presentations whether they describe the same group or not. This leads us to the decision problems, first formulated by Max Dehn, which can be solved i

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Group Presentations,presentations whether they describe the same group or not. This leads us to the decision problems, first formulated by Max Dehn, which can be solved in many cases in a very geometric way as described in Chap. ..

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Abelian and Solvable Groups,roups is given. The last section introduces solvable groups, which are important in connection with field extensions in Galois theory. We do not go into field extensions here, but solvable groups are also interesting within group theory.

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1615-2085 e examples and practice exercises.This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects...Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective t

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Springer Undergraduate Mathematics Serieshttp://image.papertrans.cn/v/image/983728.jpg

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https://doi.org/10.1007/978-3-662-69365-0Algebra; Euclidean geometry; Hyperbolic Geometry; textbook on group theory; Homomorphism; Quotient group;