Schreier generator ($tg{\overline{tg}}^{-1}$)

For a subgroup $H$ of a group generated by a set $S$, choose representatives $t$ of right cosets $Ht$. If $\overline{tg}$ represents $Htg$, then $tg{\overline{tg}}^{-1}$ lies in $H$. These Schreier generators generate $H$: inserting successive coset representatives along a word telescopes the word into such factors. Lifted relators can be rewritten in the same factors.