Definition:Group Action/Also known as

Group Action: Also known as
Some sources refer to a group action as a $G$-action, and refer to the set $X$ upon which it acts as a $G$-set.

Some sources use $g \wedge x$ for $g * x$, while some use $g \cdot x$.

Some sources introduce the concept with the notation $\map {\phi_g} x$ for $g * x$, before progressing to the latter notation.

There is little consistency in the literature; $*$ appears to be popular.

$\wedge$ is not generally preferred, because its other uses are somewhat specialized.