Is there any method to find order of Jacobson Radical of any ring that is non semi simple? Actually i have to find order of Jacobson radical of Group algebra $F_{3^n}(GL_2(Z_3))$. Is there any way by using GAP. Please help me.. Thanks.
2026-03-25 06:21:44.1774419704
How to find order of Jacobson Radical
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Lets assume (as in your examples) that the ring is in fact an algebra. Since the Jacobson radical is the maximal nilpotent ideal, you can use
RadicalOfAlgebra, i.e.RadicalOfAlgebra(GroupRing(GF(3),GL(2,3)));
In the example the codimension 28 agrees with the degrees (1,1,2,2,3,3) of the Brauer characters.