Linear independence of cables in the knot concordance group

We produce infinite families of knots $\{K^i\}_{i\geq 1}$ for which the set cables $\{K^i_{p,1}\}_{i,p\geq is linearly independent in knot concordance group. arrange that these examples lie arbitrarily deep solvable and bipolar filtrations group, denoted by $\{F_n\}$ $\{B_n\}$ respectively. As a consequence, this result cannot be reached any combination algebraic invariants, Casson-Gordon Heegaard-Floer invariants such as tau, epsilon, Upsilon. give two applications result. First, n>=0, there exists an family each fixed i, $\{K^i_{2^j,1}\}_{j\geq 0}$ basis rank summand $F_n$ $\{K^i_{p,1}\}_{i, p\geq $F_{n}/F_{n.5}$. Second, n>=1, we filtered counterexamples to Kauffman's conjecture on slice constructing smoothly with genus one Seifert surfaces where derivative curve has nontrivial Arf invariant other both $F_n/F_{n.5}$ $B_{n-1}/B_{n+1}$. also topologically but not slice.