Schreier generator
= Schreier generator
{c}
{title2=$t g\,\overline{t g}^{-1}$}
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.