[−][src]Trait mathru::algebra::abstr::Group

pub trait Group<O: Operator>: Loop<O> + Monoid<O> { }

A Group is a triple $(\mathbb{M}, \circ, e)$, composed by a set $\mathbb{M}$ and a binary inner operation $\circ$ and the element $e \in \mathbb{M}$ # Definition

\circ: \mathbb{M} \times \mathbb{M} \rightarrow \mathbb{M} , (x, y) \mapsto x \circ y

associativity
$\forall x, y, z \in \mathbb{M}$: $x \circ (y \circ z) = (x \circ y) \circ z$ 2. $e$ neutral element(identity)
$\forall x \in \mathbb{M}$: $x \circ e = e \circ x = x$

$x^-1 \in \mathbb{M}: x^⁻1 \circ x = x \circ x^-1 = e$