Notations in Group Theory

NOTATION

We use standard Bourbaki notations:

\(\mathbb{N}=\{0,1,2,\ldots\}\)

\(\mathbb{Q}\) is the field of rational numbers

\(\mathbb{R}\) is the field of real numbers

\(\mathbb{C}\) is the field of complex numbers

\(\mathbb{F}_q\) is a finite field with \(q\) elements where \(q\) is a power of a prime number

In particular, \(\mathbb{F}_p=\mathbb{Z}/p\mathbb{Z}\) for \(p\) a prime number

For integers \(m\) and \(n\), \(m{\mid}n\) means that \(m\) divides \(n\), i.e., \(n \in m\mathbb{Z}\)

\(X\approx Y\) \(X\) is isomorphism to \(Y\)

\(X\simeq Y\) \(X\) and \(Y\) are canonically isomorphic (or there is a given or unique isomorphism)