  We show that every Hausdorff topological group is a group retract of a
minimal topological group. This first was conjectured by Pestov in 1983. Our
main result leads to a solution of some problems of Arhangelskii. One of them
is the problem about representability of a group as a quotient of a minimal
group (Problem 519 in the first edition of "Open Problems in Topology"). Our
approach is based on generalized Heisenberg groups and on groups arising from
group representations on Banach spaces and in bilinear mappings.
