It is known that each of the successive quotient groups of the grope and solvable
filtrations of the knot concordance group has an infinite-rank subgroup. The
generating knots of these subgroups are constructed using iterated doubling
operators. In this paper, for each of the successive quotients of the filtrations we give
a new infinite-rank subgroup which trivially intersects the previously known
infinite-rank subgroups. Instead of iterated doubling operators, the generating
knots of these new subgroups are constructed using the notion of algebraic
–solutions,
which was introduced by Cochran and Teichner. Moreover, for any slice knot
whose Alexander polynomial has degree greater than
, we
construct the generating knots so that they have the same derived quotients
and higher-order Alexander invariants up to a certain order as the knot
.
In the proof, we use an
–theoretic
obstruction for a knot to being
–solvable given by Cha,
which is based on
–theoretic
techniques developed by Cha and Orr. We also generalize and use the notion of algebraic
–solutions to the
notion of
–algebraic
–solutions, where
is either the rationals
or the field of
elements for a prime
.
