algebra, a prosolvable group (less common: prosoluble group) is a group that is isomorphic to the inverse limit of an inverse system of solvable groups. Equivalently...

composition series is a p-group or has order prime to p. A finite group is solvable iff it is p-solvable for every p. Prosolvable group Milne. Field Theory...

{Gal} \left({\overline {\mathbb {Q} _{p}}}/\mathbb {Q} _{p}\right)} is prosolvable. Q p {\displaystyle \mathbb {Q} _{p}} contains the n-th cyclotomic field...

Jarden, Prosolvable subgroups of free products of profinite groups, Communications of Algebra 22 (1994), 1467-1494. M. Jarden, On free profinite groups of...