Two-torsion in the grope and solvable filtrations of knots.

We study knots of order in the grope filtration and the solvable filtration of the knot concordance group. We show that, for any integer , there are knots generating a subgroup of . Considering the solvable filtration, our knots generate a subgroup of distinct from the subgroup generated by the previously known -torsion knots of Cochran, Harvey, and Leidy. We also present a result on the -torsion part in the Cochran, Harvey, and Leidy's primary decomposition of the solvable filtration. [ABSTRACT FROM AUTHOR]