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Cochran–Orr–Teichner introduced in [‘Knot concordance, Whitney towers and  L  2 ‐signatures’,  Ann. of Math.  (2) 157 (2003) 433–519] a natural filtration of the smooth knot concordance group   C…  ⊂   F   n  +  1    ⊂   F   n  .5    ⊂   F  n   ⊂  …  ⊂   F  1   ⊂   F   0.5    ⊂   F  0   ⊂  C  ,    called the ( n )‐ solvable filtration . We show that each associated graded abelian group{G  n   =   F  n   /   F   n  .5    |  n  ∈  N    }   ,  n  ⩾  2   ,  n  ⩾ 2, contains infinite linearly independent sets of elements of order 2 (this was known previously for  n  = 0, 1). Each of the representative knots is negative amphichiral, with vanishing  s ‐invariant,  τ ‐invariant,  δ ‐invariants and Casson–Gordon invariants. Moreover, each is slice in a rational homology 4‐ball. In fact we show that there are many distinct such classes inG  n    , distinguished by their Alexander polynomials and, more generally, by the torsion in their higher‐order Alexander modules.

2‐torsion in the n ‐solvable filtration of the knot concordance group