Kevin Wampler wrote:
> Orchid XP v8 wrote:
>> Of course, intuitively, it totally makes sense that the order of a 
>> subgroup would have to be a factor of the group's order. I just 
>> thought that every group could be split into subgroups. So I guess 
>> there are large non-prime groups that don't have any [nontrivial] 
>> subgroups then?
> 
> This is not actually true either.  If a group G is of order n, then G 
> does have a subgroup of every order which is a *prime* factor of n. It's 
> just that there's no guarantee for composite factors.

So, in summary, G *definitely* has subgroups for every prime factor, and 
*might* have subgroups for some or all of the composite factors as well?

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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