Math Is Fun Forum

Sekky

Member

Registered: 2007-01-12

Posts: 181

Simple Groups

Is there any discernable property of simple groups that can be used to quickly verify whether a group is simple other than to blast through trying to find normal subgroups?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Simple Groups

It will become much easier to tell if a group is simple or not once you learn Sylow-theory.  Sylow-theory ("see-low theory") is really just an awesomely powerful theorem, and it's primary use is to prove whether or not all groups of a certain order are simple (at least in my experience).

Other than that, I know of no way to simply tell if a group is simple or not.  Obvioiusly any abelian group with a proper non-trivial subgroup is not simple.

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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..."