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Infinite dihedral group

 Home Mathematics Fields of mathematics Fields of abstract algebra Group theory Infinite group theory
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The infinite dihedral group, usually denoted as \( D_{\infty} \) or sometimes \( D_{\infty}^* \), is a mathematical structure in group theory that extends the concept of the dihedral groups. While the finite dihedral group \( D_n \) represents the symmetries of a regular polygon with \( n \) sides (including rotations and reflections), the infinite dihedral group captures symmetries of an infinite linear arrangement.

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  1. Infinite group theory
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