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December 7th, 2016, 01:18 PM  #1 
Newbie Joined: Dec 2016 From: England Posts: 7 Thanks: 0  No simple groups of size
Please help  what do I do when 128 is just 2 to the power 7?
Last edited by skipjack; January 14th, 2017 at 08:03 PM. 
December 7th, 2016, 08:22 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics 
Can you find an element of order 2? If so, it generates a subgroup of order 2, call this $H$. What can you say about $G/H$?

January 10th, 2017, 11:40 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
"When" is strange wording 128 is always !

January 14th, 2017, 06:11 PM  #4 
Member Joined: Jan 2016 From: Athens, OH Posts: 93 Thanks: 48 
SDK's answer is confusing at best. Given a group G or order 128, it is not necessarily the case that any subgroup of order two is normal. So you need to know that any finite pgroup (group of order a power of a prime p) has a nontrivial center. So if G is nonabelian, its center is a proper normal subgroup. So now you can assume G is abelian. By Cauchy's theorem there is a subgroup H of order 2; this H is now a proper normal subgroup. 

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