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*.