Group Actions

Dinesh Khattar () and Neha Agrawal ()
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Dinesh Khattar: University of Delhi, Department of Mathematics
Neha Agrawal: University of Delhi, Department of Mathematics

Chapter Chapter 10 in Group Theory, 2023, pp 271-302 from Springer

Abstract: Abstract We outline group action and substantiate with various examples. Group action is a potent tool which can be employed to gain insight into the structure of groups. It is a representation of the elements of a group as symmetries of a set. Many groups have a natural group action coming from their construction; e.g. the dihedral group D4 acts on the vertices of a square because the group is given as a set of symmetries of the square. A group action of a group on a set is a generalization of this idea, which can be used to derive useful facts about both the group and the set it acts on.

Date: 2023
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DOI: 10.1007/978-3-031-21307-6_10

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