nLab
structure group

Idea

For $G$ a geometric group (e.g. a topological group or Lie group) and $P\to X$ a $G$-principal bundle, one says that $G$ is the structure group of $P$.

More generally, and less tautologically, if $V\to X$ is a $G$-associated bundle then one says that $V$ has structure group $G$.

Related concepts

• reduction of structure group

• gauge group