|December 7th, 2016, 02:18 PM||#1|
Joined: Dec 2016
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 09:03 PM.
|December 7th, 2016, 09:22 PM||#2|
Joined: Sep 2016
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 14th, 2017, 07:11 PM||#4|
Joined: Jan 2016
From: Athens, OH
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 p-group (group of order a power of a prime p) has a non-trivial center. So if G is non-abelian, 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.
|groups, simple, size, sylow|
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