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.