Let $G$ be a finitely presented group and $H$ be its subgroup. Suppose they are stored in GAP such that $IsSubset( G, H )$ returns true. However, they may not be stored as fp groups. When I do $Display( G )$, I obtain some presentation $pr$ of $G$. I can do $Display( H )$ as well. Is it true, that the generators of $H$ returned by this function will correspond to the presentation $pr$ of $G$?
2026-03-26 23:59:59.1774569599
Display subgroup in GAP
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If $H$ has generators (or you enforce them via
GeneratorsOfGroupthese are of course words in the generators of $G$, otherwise one would not know what the subgroup is. Thus in this sense they correspond to $G$. There is no guarantee that they are particularly nice or the ones you would find by a proof by hand.However
Displaywill not calculate a new presentation in the subgroup generators (which seemed in your previous question what you were looking for).