Let $\pi:P\to M$ be a smooth principal $G$-bundle with right action $P\times G\to P$, $(q,a)\mapsto q a$, and let $\omega$ be a principal connection on $P$. For $x\in M$ and $p\in P_x:=\pi^{-1}(\{x\})$, define the holonomy group at $p$ by
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\begin{align*}
\operatorname{Hol}_p(\omega):=\{g\in G:\text{ there exists a piecewise smooth loop }\gamma:[0,1]\to M\text{ with }\gamma(0)=\gamma(1)=x\text{ and }\operatorname{PT}^{\omega}_{\gamma}(p)=p g\}.
\end{align*}