Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493375 | Journal of Algebra | 2005 | 17 Pages |
Abstract
If Î is an indecomposable, non-maximal, symmetric order, then the idealizer of the radical Î:=Id(J(Î))=J(Î)# is the dual of the radical. If Î is hereditary, then Î has a Brauer tree (under modest additional assumptions). Otherwise Î:=Id(J(Î))=(J(Î)2)#. If Î=ZpG for a p-group Gâ 1, then Î is hereditary iff Gâ
Cp and otherwise [Î:Î]=p2|G/(Gâ²Gp)|. For Abelian groups G, the length of the radical idealizer chain of ZpG is (nâa)(paâpaâ1)+paâ1, where pn is the order and pa the exponent of the Sylow p-subgroup of G.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Gabriele Nebe,