2-torsion in the grope and solvable filtrations of knots

We study knots of order 2 in the grope filtration $\{{\text{G}}_h\}$ and the solvable filtration $\{{\text{F}}_h\}$ of the knot concordance group. We show that, for any integer $n\ge 4$, there are knots generating a ${\mathbb{Z}}_2^{\mathrm{\infty }}$ subgroup of ${\text{G}}_n\mathrm{/}{\text{G}}_{n.5}$. Considering the solvable filtration, our knots generate a ${\mathbb{Z}}_2^{\mathrm{\infty }}$ subgroup of ${\text{F}}_n\mathrm{/}{\text{F}}_{n.5}$ $(n\ge 2)$ distinct from the subgroup generated by the previously known 2-torsion knots of Cochran, Harvey, and Leidy. We also present a result on the 2-torsion part in the Cochran, Harvey, and Leidy’s primary decomposition of the solvable filtration.