The concordance group of algebraically slice knots is the subgroup of the classical
knot concordance group formed by algebraically slice knots. Results of Casson and
Gordon and of Jiang showed that this group contains in infinitely generated free
(abelian) subgroup. Here it is shown that the concordance group of algebraically slice
knots also contain elements of finite order; in fact it contains an infinite subgroup
generated by elements of order 2.