[GAP Forum] Subgroups of prime power elements

[Sandeep Murthy]

Dear Forum members,

if G is a p-group, could I please know what commands I must use to 
define the subgroup of G generated by all p^th powers of elements of
G, and also the subgroup of G generated by all elements of order p?
More generally, how can one define in G the subgroup generated by 
p^k th powers of its elements, and the subgroup generated by its 
elements of order p^k?

For my purposes, the groups G I am studying are nonabelian 
2-groups.

Sincerely, Sandeep.