Let $G$ be a group and $V$ be a representation of $G$. We say that $V$ is a cyclic representation if there exists $v \in V$ such that $ \{ g \cdot v \ | \ g \in G \} $ generates $V$. Is there a common name for such an element?
I know that as a $\mathbb{k}G$-module (which is an equivalent construction), it is called a generator. But because I work in representation theory (and I want to keep this approach in my article), $V$ is a vector space, so in that setting, generator is the name of an element of the set $ \{ g \cdot v \ | \ g \in G \} $, and of many other sets. Is there another name?