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Approximating the fusion map.


Let tex2html_wrap_inline3539 be a complete set of representatives of conjugacy classes of maximal subgroups of G and, for tex2html_wrap_inline3543 , denote by tex2html_wrap_inline3545 the inclusion map from tex2html_wrap_inline3547 into G, given by tex2html_wrap_inline3551 for each tex2html_wrap_inline3553 . For each tex2html_wrap_inline3555 , let tex2html_wrap_inline3557 be the poset of conjugacy classes of subgroups of tex2html_wrap_inline3559 and let tex2html_wrap_inline3561 be the poset of conjugacy classes of subgroups of G. Then each inclusion map tex2html_wrap_inline3565 induces a map tex2html_wrap_inline3567 mapping the conjugacy class tex2html_wrap_inline3569 of subgroups of tex2html_wrap_inline3571 to the conjugacy class tex2html_wrap_inline3573 of subgroups of G. Denote by tex2html_wrap_inline3577 the disjoint union


and let tex2html_wrap_inline3579 be the union of the maps tex2html_wrap_inline3581 given by


Let tex2html_wrap_inline3583 . Then m is of the form tex2html_wrap_inline3587 for some tex2html_wrap_inline3589 . Denote tex2html_wrap_inline3591 and tex2html_wrap_inline3593 . Then the induction formula 2.2 can, for any subgroups tex2html_wrap_inline3595 , be written as


where the sum ranges over all tex2html_wrap_inline3597 such that tex2html_wrap_inline3599 .

In this section we discuss how to determine this fusion map j.

Götz Pfeiffer Wed Oct 30 09:52:08 GMT 1996