Let be a complete set of representatives of conjugacy classes of maximal subgroups of G and, for , denote by the inclusion map from into G, given by for each . For each , let be the poset of conjugacy classes of subgroups of and let be the poset of conjugacy classes of subgroups of G. Then each inclusion map induces a map mapping the conjugacy class of subgroups of to the conjugacy class of subgroups of G. Denote by the disjoint union
and let be the union of the maps given by
Let . Then m is of the form for some . Denote and . Then the induction formula 2.2 can, for any subgroups , be written as
where the sum ranges over all such that .
In this section we discuss how to determine this fusion map j.