Abstract:
It is proved that there exist uncountably many nonisomorphic
pro-$p$-groups admitting presentations with two generating elements
and one defining relation in the variety of metabelian
pro-$p$-groups.
Also we give information on pro-$p$-groups with a
single relation in varieties of nilpotent pro-$p$-groups.
Keywords:pro-$p$-group, variety of metabelian
pro-$p$-groups, variety of nilpotent pro-$p$-groups.