Axiom:Group Action Axioms
Jump to navigation
Jump to search
Definition
Let $\struct {G, \circ}$ be a group which acts on a set $X$.
The properties that define the group action $*: G \times X \to X$ are summarised as:
\((\text {GA} 1)\) | $:$ | \(\ds \forall g, h \in G, x \in X:\) | \(\ds g * \paren {h * x} = \paren {g \circ h} * x \) | ||||||
\((\text {GA} 2)\) | $:$ | \(\ds \forall x \in X:\) | \(\ds e * x = x \) |
These properties can be referred to as the group action axioms.