Math Is Fun Forum

laipou

Member

Registered: 2009-09-19

Posts: 24

solvable group

Let G be a solvable group of order n.
Show that there is a sequence of subgroups G = G0 > G1 >...>Gn ={e} such that for all i,
Gi+1 is normal in Gi and Gi/Gi+1 is cyclic of order pi for some prime pi.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: solvable group

Have you heard of the Jordan-Holder theorem?  Refine your series until you get to your conclusion.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

laipou

Member

Registered: 2009-09-19

Posts: 24

Re: solvable group

I get it ! thx.