Title: all
Tags: ch1 ch1.1

The general linear group of degree \(n\) (mathematically \(\text{GL}_n(\mathbb{R})\)) is the set of \(n \times n\) matrices which have a nonzero determinant, with the operation matrix multiplication \(\times\).

The multiplicative group modulo \(p\) (mathematically \((\mathbb{Z}/p\mathbb{Z})^{\times}\)) is the set of integers from 1 to \(p-1\), \(p\) prime, with the operation of multiplication modulo \(p\).

The symmetric group of \(n\) elements (written \(S_n\)) is the set of permutations of a set with \(n\) elements, with the operation of permutation composition \(\circ\).

The dihedral group of order \(2n\) (written \(D_{2n}\)) is the set of symmetries of a regular \(n\)-gon (including rotations and reflections) with the operation of function composition.