How i can show that group of order 250 is a solvable group ?

|G| = 2*(5^3)

But i count show that (5^3)/{e} is abelian group

Thanks

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- Jan 1st 2010, 06:55 AMs.lateralussolvable group
How i can show that group of order 250 is a solvable group ?

|G| = 2*(5^3)

But i count show that (5^3)/{e} is abelian group

Thanks - Jan 1st 2010, 08:27 AMNonCommAlg
- Jan 1st 2010, 08:41 AMNonCommAlg
a more direct method: again let be the Sylow 5-subgroup of we know that contains subgroups such that now look at this subnormal series:

- Jan 1st 2010, 08:49 AMs.lateralus
How do you know that 5^2 is normal in 5^3 ?

- Jan 1st 2010, 09:21 AMDinkydoeCode:
`How do you know that 5^2 is normal in 5^3 ?`

There's a little theorem that states that any sub-group with index p is normal - Jan 1st 2010, 09:44 AMtonio