[GAP Forum] Is there a routine to compute the Jacobson radical of a finite group?

[Stephen Linton]

For at least some groups, the obvious commands work:

for instance

gap> g := SmallGroup(1536,10^6);
<pc group of size 1536 with 10 generators>
gap> Intersection(MaximalNormalSubgroups(g));
Group([ f6, f7, f8, f9 ])
gap> s := TransitiveGroup(24,1000);
t24n1000
gap> Intersection(MaximalNormalSubgroups(s));
<permutation group of size 96 with 6 generators>

I’m not sure what the limitations of the available methods fro MaximalNormalSubgroups are, 
nor whether a method targeted directly at the Radical could be significantly more efficient.

	Steve

> On 21 Nov 2015, at 21:20, Will Chen <oxeimon at gmail.com> wrote:
> 
> Here by Jacobson radical I mean the intersection of all maximal normal
> subgroups.
> 
> Thanks,
> 
> - Will
> 
> -- 
> 
> William Yun Chen
> Ph.D. Student & Graduate Teaching Associate
> Department of Mathematics
> Pennsylvania State University, University Park, PA, 16801
> chen_w at math.psu.edu
> oxeimon at gmail.com
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