What Are the Key Differences Between C2 and C4 Operations in Group Theory?

jaejoon89
Messages
187
Reaction score
0
What is the difference between the C2 and C4 operations on one hand for Oh and on the other, the 3C2=(C4)2?
 
Physics news on Phys.org
Please can you explain your notation, and what you've done. I.e. follow the homework forum guidelines.
 

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

I Isomorphisms between C4 & Z4 Groups
Replies
1
Views
2K
Understanding the notation in Group Theory
Replies
24
Views
5K
What Is the Galois Group of x^5 - 1 Over Q?
Replies
7
Views
7K
Chemistry Expanding and Naming of Abbreviated Chemical Formulas
Replies
1
Views
2K
Engineering Charge Redistribution in a Capacitor Bank/DAC
Replies
22
Views
5K
Are all order 4 groups only isomorphic to C4 or C2+C2?
Replies
3
Views
7K
Group Theory: Is the following a valid Group?
Replies
7
Views
1K
Insights Groups, The Path from a Simple Concept to Mysterious Results
Replies
17
Views
8K
I Dfns group action & group, written in terms of the other
Replies
26
Views
422
I Differences between left vs right actions in some group theory questions
Replies
1
Views
130

Hot Threads

Recent Insights

Back
Top