Two-torsion in the grope and solvable filtrations of knots

Abstract

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