  Let K be a knot in the 3-sphere with 2-fold branched covering space M. If for
some prime p congruent to 3 mod 4 the p-torsion in the first homology of M is
cyclic with odd exponent, then K is of infinite order in the knot concordance
group. As one application, recall that the n-twisted double of an arbitrary
knot has order 4 in Levine's algebraic concordance group if and only if n is
positive and some prime congruent to 3 mod 4 has odd exponent in 4n+1; we show
that all such knots are of infinite order in the knot concordance group. As a
second application, the 2-bridge knot K(r,s) has infinite order in the knot
concordance group if some prime congruent to 3 mod 4 has odd exponent in r.
