Recent content by millwallcrazy

I was just curious as to how I can show the following properties of the Gamma Function, they came up in some lecture notes but were just stated? Notation: G(z) = Gamma function 2^(z) = 2 to the power of z I = Integral from 0 to infinity (1) G(z)*G(1-z) =...

i'm having trouble to show that if P: G1 --> G2 is a group homomorphism, then the image, P(G1) = {g belongs to G2 , s.t. there exists h belonging G1 , P(h) = g}, is a subgroup of G2 Also: Let G be a group, and Perm(G) be the permutation group of G. Show that the map Q : G --> Perm(G) g...

Can we just multiply both sides on the left by g-1 and the right by g so that it now becomes the required result? i.e. H is a subset of g-1Hg?

For a group to be normal subgroup of another doesn't it mean gHg-1 belongs to H? I don't see how this would help?

I have now come to this conclusion: i need to show that (ab)H = (a'b')H First step: (ab)H = aHbH = a'Hb'H = (a'b')H Is that how to show its well defined or is there anything that i wasnt allowed to do?

Thanks for the help, i was just wondering how i go about showing that it was well defined. I tried to use the facts that were given I didn't know what to do once (aH)(bH) = (ab)H...is the next step to say that this is ab'H?

Help with permutation groups... How do i show that if P: G1 --> G2 is a group homomorphism, then the image, P(G1) = {g belongs to G2 , s.t. there exists h belonging to G1 , P(h) = g}, is a subgroup of G2 Also if we let G be a group, and Perm(G) be the permutation group of G. How do i show...

Hi guys I was just wondering whether anyone could help me with Group Theory I am trying to prove that G/H is a group (where G is a group and H is a normal subgroup of G) I know that i need to go through the 4 properties, Identity, inverse, Associativity and Closure but I'm not sure...

I know that hte MGF is = the E[e^tx] How do i show that if i take a sample (X1;X2; : : :Xn) from the exponential density f(x) = A*e^(-Ax), then the sum Z = sum(Xi) has the gamma density? I found that the MGF for the exponential was A/(t-A) if that helps Thanks

f(x) = 3(x^2)/(C^3) 0 < x < C = 0 otherwiseLet the mean of the sample be Xa and let the largest item in the sample be Xm. What is the cumulative distribution for Xm?

No i am not sure why G/H only consists of only 2 precise elements in (2)? Could you please explain why?

in (2) the groups are infinite, how does that mean that [G:H] = 2?

Just a few things. What is [G : H]? Why is it that you said the identity is H? As the only other coset aside from H is {b,ab, (a^2)b} how does this then determine what G/H is? you have only found two cosets...and not the group G/H? Last thing. How is this identical to (2) because GL...

Does anybody know a general method to find the Group G/H (Where G is a Group and H is a subgroup of G) For example (1) What is the group S3/H ? S3 = {e, a, a^2, b, ab, (a^2)b} (Permutation group of order 6) H =< a >= {e, a, a^2} is a cyclic subgroup of G (2) What is the group...