| Symbol |
Description |
Location |
| \(\N\) |
The set of natural numbers. |
Example 1.2 |
| \(\Z\) |
The set of integers. |
Example 1.2 |
| \(\Q\) |
The set of rational numbers. |
Example 1.2 |
| \(\R\) |
The set of real numbers. |
Example 1.2 |
| \(\C\) |
The set of complex numbers. |
Example 1.2 |
| \(Y^X\) |
The set of all set functions with domain \(X\) and codomain \(Y\text{.}\)
|
Definition 1.3 |
| \(\End_{\Set}(X)\) |
The set of set functions \(f \colon X \to X\text{.}\)
|
Definition 1.4 |
| \(\operatorname{M}_{m \times n}(\R)\) |
The set of \(m \times n\) matrices with entries from \(\R\text{.}\)
|
Definition 1.8 |
| \(\operatorname{M}_n(\R)\) |
The set of \(n \times n\) matrices with entries from \(\R\)
|
Definition 1.8 |
| \(1\) |
The identity for a multiplicative binary operation. |
Paragraph |
| \(0\) |
The identity for an additive binary operation. |
Paragraph |
| \(\Q^\times\) |
The multiplicative group of non-zero rational numbers. |
Example 2.24 |
| \(\R^\times\) |
The multiplicative group of non-zero real numbers. |
Example 2.24 |
| \(\operatorname{GL}_n(\R)\) |
The multiplicative group of invertible matrices with entries from \(\R\)
|
Example 2.25 |
| \(S_X\) |
The symmetric group on the set \(X\)
|
Example 2.26 |
| \(G \cong H\) |
Isomorphism of groups |
Definition 3.11 |
| \(\overline{a}\) |
The residue class of \(a \in \Z\) modulo \(n\)
|
Paragraph |
| \(\C^\times\) |
The multiplicative group of non-zero complex numbers. |
Paragraph |
| \(S_n\) |
The symmetric group on the set \(\{1,2,3,\ldots,n\}\)
|
Paragraph |
| \(H \leq G\) |
\(H\) is a subgroup of \(G\)
|
Definition 6.1 |
| \(\phi(K)\) |
The image of \(K\) under \(\phi\)
|
Definition 6.9 |
| \(\phi^{-1}(L)\) |
The preimage of \(L\) under \(\phi\)
|
Definition 6.13 |
| \(\langle g \rangle\) |
The subgroup generated by \(g \in G\)
|
Theorem 7.12 |
| \(\abs{g}\) |
The order of \(g\) in \(G\)
|
Definition 7.17 |
| \(\prod_{i \in I} \zeta_i\) |
The morphism induced by the universal property for the product |
Remark 9.6 |
| \(a \equiv_\ell b \pmod{H}\) |
\(a\) is left equivalent to \(b\) modulo the subgroup \(H\)
|
Definition 10.1 |
| \(gH\) |
Left translate of \(H\) by \(g\text{.}\)
|
Definition 10.5 |
| \(G/H\) |
The set of left cosets of \(H\) in \(G\)
|
Definition 10.8 |
| \(Hg\) |
Right translate of \(H\) by \(g\text{.}\)
|
Definition 10.13 |
| \(H \backslash G\) |
The set of right cosets of \(H\) in \(G\)
|
Definition 10.14 |
| \(\abs{G : H}\) |
The index of \(H\) in \(G\)
|
Definition 10.16 |
| \(R^\times\) |
The multiplicative group of units in the ring \(R\)
|
Definition 13.20 |
| \(Ra\) |
The ideal generated by \(a\)
|
Definition 17.8 |
