pure subgroup
a subgroup S of a group G such that, whenever an element of S has an nth root in G, it necessarily has an nth root in S
en-US/ˈpjʊɹ ˈsʌbˌɡɹup/
en-GB/ˈpjɔː ˈsʌbɡɹuːp/
a subgroup S of a group G such that, whenever an element of S has an nth root in G, it necessarily has an nth root in S