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1. Permutation Groups

Is it really that simple? lol This is what I was thinking, but I wasn't sure how to connect the idea to permutations. Can I just say "a is an even permutation" and "b is an even permutation" thus "a*b is also an even permutation"? Because, if this is true and if I assume that a and b are...
2. Alternating Group

For any elements σ, τ ∈ Sn, show that στσ-1τ-1 ∈ An.
3. Permutation Groups

Homework Statement Show that if G is any group of permutations, then the set of all even permutations in G forms a subgroup of G. I am not sure where to start - I know there is a proposition that states this to be true, but I know that is not enough to prove this statement.
4. Abstract Algebra question

Homework Statement Let G be a group with pk elements, where p is a prime number and k is greater than or equal to 1. Prove that G has a subgroup of order p. The Attempt at a Solution I attempted to prove this by showing that the conditions for a set to be subgroup form a subgroup of order...
5. Calculate charge and current

Homework Statement The region between concentric conducting spheres is filled with a material with conductivity σ and dielectric constant k. The inner sphere (radius a) is connected to the positive terminal of a battery with emf Vo, and the outer sphere (radius b) is connected to the...
6. Ohm's Law - coaxial conducting cylinder, find resistance and surface charge density

Homework Statement Consider two coaxial conducting cylinders with radii a and 3a and length L. The region a<r<2a is filled with a material of conductivity σ1, and the region 2a<r<3a has conductivity σ2. (Assume ε1=ε2=εo.) The inner cylinder is held at potential V0 and the outer cylinder at...
7. Ohm's Law - current within parallel plate capacitor imbedded in a large volume

Homework Statement A parallel plate capacitor with plates of area A and separation d is imbedded in a large volume filled with a material with electric conductivity σ. Determine the total current I if the two capacitor plates are maintained at a potential difference Vo. Explain how such a...
8. Forced undamped non-linear oscillator

Homework Statement The equation of motion of a forced undamped non-linear oscillator of unit mass is given by a+s(x)=Focoswt. Writing s(x)=s1x + s3x3, where s1 and s3 are constant, choose the variable wt= ϕ, and for s3<<s1 assume a solution x=\sum(n=1 to ∞)(ancos[(n/3)ϕ]+bn sin[(n/3)ϕ]) to...
9. Electrostatics - spherically symmetric charge density

I apologize for taking so long to reply... thank you to everyone who posted! :-) I am working out the problem now with your suggestions. If I find myself stuck again, I will be back... and I promise not to take a year to reply next time.
10. Electrostatics - spherically symmetric charge density

Homework Statement Imagine a spherically symmetric charge density p(x) = Cr for r≤a and 0 for r>a (a) determine the electric field E(x) and potential V(r). Notice that V(r) and E(x) are continuous at r=a. (b) Now suppose additional charge is placed uniformly on the surface at r=a, with...
11. Electric current flowing through a resistor

ok, thank you!!!!!!!!!!!!!!!!!!!!!!!! :-)
12. Electric current flowing through a resistor

Ok, I dont mean to be a pain... but how do I work out the equivalent resistance between the two dots (i.e. within the two loops)? If you could explain with a little more detail, I would appreciate it. I don't expect the answer to the problem, just a more direct explanation of how to find the...
13. Electric current flowing through a resistor

Ok, so R2 and R5 are in series, so their equivalent resistance is 3ohm+3ohm=6 ohm. So, does that mean the current flowing through these 2 resistors is I=V/R, or I=10.4/6=1.73 A? And because they are in series and because it is the same current through both, that means the current through R2 is...
14. Electric current flowing through a resistor

Ok, so I have found the equivalent resistance to be 8ohm, and the current across the equivalent resistance to be I=V/R=10.4/8=1.3 A. But, I am stuck as to what to do next. I don't know why, but I feel weak as to the theory behind individual resistors and current, voltage, etc across them. :-(
15. Electric current flowing through a resistor

Homework Statement Consider the electric circuit shown in the figure. Assume that V = 10.4 V, R1 = R2 = R3 = R4 = R5 = 3.00 Ohm. What is the electric current flowing through resistor R2? I couldn't upload the figure, but you can find it on my cramster.com post...
16. Two charged capacitors cross connected to each other

Homework Statement Capacitors C1 = 6.99 mF and C2 = 1.72 mF are charged as a parallel combination across a 219 V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to positive plate...
17. I am unsure of factorials

To djeikyb: your response makes sense now. I misunderstood 1/2^n to be 1/2n. Thank you. :-) To Mark44: Thank you :-)
18. I am unsure of factorials

Well, I know from the comparison test, if An=1/(2n)! and Bn=1/2n and if An is less than Bn, and if Bn is convergent, than An is also convergent. Yet, in this case, Bn is divergent (because 1/2n is a p-series with p=1, and this is divergent.) So, the comparison test shows nothing... So, I am...
19. I am unsure of factorials

I am unsure as to how factorials should be expanded. I have \sum\stackrel{1}{(2n!)} (if what was just typed did not make sense due to html error on my part, it is supposed to say the sum of 1/(2n)!) from n=1 to infinity. I did the ratio test and found the limit to be 0, which is less than...