  The target space M for the sigma-model appearing in theories with p-branes is
considered. It is proved that M is a homogeneous space G/H. It is symmetric if
and only if the U-vectors governing the sigma-model metric are either
coinciding or mutually orthogonal. For nonzero noncoinciding U-vectors the
Killing equations are solved. Using a block-orthogonal decomposition of the set
of the U-vectors it is shown that under rather general assumptions the algebra
of Killing vectors is a direct sum of several copies of sl(2,R) algebras
(corresponding to 1-vector blocks), several solvable Lie algebras
(corresponding to multivector blocks) and the Killing algebra of a flat space.
The target space manifold is decomposed in a product of a flat space, several
2-dimensional spaces of constant curvature (e.g. Lobachevsky space, part of
anti-de Sitter space) and several solvable Lie group manifolds.
