Group Theory - specific non-abelian case

audiowize
Messages
6
Reaction score
0

Homework Statement



Let G be an Abelian group and let H+{x^3 : x is an element of G}

Find a non-Abelian group in which H is not a subgroup

Homework Equations



I wish it was that easy...

The Attempt at a Solution



I looked at the quaternion group, and some other matrix groups, but no luck so far...
 
Physics news on Phys.org
What is the first non-abelian group in any reasonable ordering?
 
The permutation group S_3.

I looked at this also... but the cubes of the individual elements seemed closed under the operation of composition, and the identity is present... Four of us have spent about 3 hours on this without much luck, any nudging is greatly appreciated!
 
You should triple-check your work, because matt is never wrong. If G=S_3, what are you thinking H is?
 
Thanks for the help guys! I'm sure glad I don't have to take exams at midnight. A fresh set of eyes in the morning and your confirmation sure helped!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Group Theory: Finite Abelian Groups - An element of order
Replies
3
Views
2K
Show that ##G\simeq \mathbb{Z}/2p\mathbb{Z}##
Replies
2
Views
1K
Subgroup of Index ##n## for every ##n \in \Bbb{N}##.
Replies
1
Views
2K
Commutator group in the center of a group
Replies
5
Views
2K
Proving Subgroups in Abelian Groups
Replies
7
Views
2K
Showing a property of Abelian groups of order n
Replies
4
Views
1K
Doubt about abelian conjugacy class
Replies
2
Views
1K
Proving that Aut(K), where K is cyclic, is abelian
Replies
5
Views
2K
Proving that an Abelian group of order pq is isomorphic to Z_pq
Replies
5
Views
3K
Abelian group as a direct product of cyclic groups
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top