Gauge group and gauge transformation in the continual theory of defects

Representation of the algebra $\mathfrak{g}(3)=t(3)\oplus so(3,\mathbb{R})$ by differential Schaefer's operators is proposed, exterior calculus of $\mathfrak{g}(3)$-valued differential forms is developed. The formulation of the requirement of local gauge invariance in the model with $\mathfrak{g}(3)$-valued fields permits one to obtain gauge transformation group of the continual theory of defects.