  An equal superposition query with |0> in the response register is used in the
"standard method" of single-query algorithms for the hidden subgroup problem
(HSP). Here we introduce a different query, the character query, generalizing
the well-known phase kickback trick. This query maximizes the success
probability of subgroup identification under a uniform prior, for the HSP in
which the oracle functions take values in a finite abelian group. We then apply
our results to the case when the subgroups are drawn from a set of conjugate
subgroups and obtain a success probability greater than that found by Moore and
Russell.
