# index

1. ### Index change

I do not understand why the indices of S, i.e. kl, change to pl, upon differentiation: d/dcp* (c†Sc) = d/dcp* ("sum from k to N" "sum from l to N" ck*Sklcl) = "Sum from k to l" Splcl Here, * indicates complex conjugation. Differentiating should leave Sc as this part is constant. I assume...
2. ### Index of Z(G) in G

Let G be a finite non-abelian 2-group. If \forall x\in G: [G:C_G(x)]=2 then how can we conclude that [G:Z(G)]=4? (where Z(G) is the center of group.)
3. ### (Q,+) cannot have a subgroup of index 2

I want to prove the group (Q,+) cannot have a subgroup of index 2. I assume H is the subgroup of index 2.And k1 k2 k3 are three rational number, satisfying k1 +k2 =k3 and they don't belong to H. If we can show there always exist such three number, it is easy to show the union H and k1H is not...
4. ### The table below shows the consumer price index (CPI) every two years from 1980...

I got y=4.467x-8760.425 im not sure if that's right. Please let me know. Thank you!
5. ### Express in Index and Surd Notation

If , express b in index and surd notation in terms of a and c My answer was: The book's answer is: Can someone please explain to me how 0.4 can equal 5/2, or is this a mistake?
6. ### Trouble understanding

Hi, today I came across an expression my college claims it tells us about the average index value i of a random variable Xi. The expression is: AI = \frac{\sum_{i}^{n} i \times X_{i}}{\sum_{i}^{n} X_{i}} However I am having problems understanding it, especially the part about dividing the...
7. ### Index numbers

What is the easiest way to work out what the last 2 digits are in the expansion 5^2012? without a calculator!
8. ### Cube Root Index Division Q

So I've been doing indices all morning and along pops this question: Maybe my brain is hurting and I need a break, but how the fudge does this equal '2'?
9. ### Sigma or sum with index or indicies

I know how to create a sigma sign for a sum - use the large operator \sum But how do you show an index, say i running from, say, 1 to n Further, how do you neatly create two or more indices Would appreciate any help in this matter Peter
10. ### Index Number related question...

The sale values (output quantity multiplied by price) for four types of product of a company at current price and 1998 price arc as follows: (RM million) Sale value at current price Sale value at 1998 price Type of product 1998 2009 2010 2009 2010 A 50 120 175 100...
11. ### Cycle index for rotation

Consider a square where there are points on the four corners and the four midpoints. Find \hat{C}(r,b) using the cycle index for the group D4. The identity has 8 cycles of length 1; the three rotations have 2 cycles of length 4; the reflections have 2 cycles of length 1 and 3 cycles of length...
12. ### Radical Equations (and Extraneous Roots?)

Hello. I am having trouble understanding the logic behind the property that states radical expressions with even-number indices cannot be equal to a negative value. Property: nth-root(xn) = |x|, if n is an even number. Let's take sqrt(25) for example: sqrt(25) = 5 is a valid statement, but...
13. ### 2 similar questions dealing with symmetric groups, Sylow, finding index and order...

"If G is a subgroup of the symmetric group S_n which contains an odd permutation, then G is a subgroup of index 2" "If G is a group of order (2^k)m, m odd, and the Sylow 2-subgroups of G are cyclic, then G has a normal subgroup of order m. Hint: Let G act on G by left multiplication and apply...
14. ### abstract algebra subgroups of finite index

Let H be a subgroup of finite index in G. Show that the intersection of all conjugates of H is a normal subgroup of finite index in G.
15. ### I need power series help and I don't get when to change the index

The problem: arctan(x/3) I assume you derive it: 1/(1+(x/3)²) then put it in the proper formation: 1/(1- (-x/3)²) so then I get the sigma of -1^2n -x/3²^n and then I have to take the integral? I just don't get what to do, like the proper formation. Why do I have to keep the -1 and -x/3...
16. ### Fractional Index Notation Help

Please See the above Picture too see the Question Many Thanks
17. ### Maths Formula Help (Kogut and Singh Index) Thesis Level work complex

Ok, i am trying to work out the cultural distance between Peru and Denmark for my Thesis. The formula is: Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting Instead of United States the Scores of Peru need be entered. Peru Scores: Dimension one: Power Distance 64 Dimension...
18. ### Einstein notation index order

In Einstein notation, is it important in which order the indexes are placed? For example, are the two expressions {a^i}_j and {a_j}^i equivalent to each other?
19. ### Using index laws to simplify this equation

Could anyone help me simplify this equation using index laws:
20. ### Family and the role and nature of the 'index'

I am seekinhg to understand example 4 on page 9 of Cohn's book "Introduction to Ring Theory" The example needs a clear understanding of the nottion of a family which Cohn briefly introduces on page 3 where he defines the notion of a set and members of a set and then defines a family mentioning...