I am taking a course in Dynamics/Chaos and I am trying to prove conjugacy between the logistic and quadratic functions. I have some ideas, but cannot get the proof to work. Attached is a word document with the functions and problem.
Let G be a group, and let H be a subgroup of G. Prove that H is a normal subgroup if and only if H can be expressed as the union of conjugacy classes of G.
The class equation of a group G is 1+4+5+5+5.
a) Does G have a subgroup of order 5? If it does, is it a normal subgroup?
b) Does G have a subgroup of order 4? If it does, is it a normal subgroup?
c) Determine the possible class equations of nonabelian groups of order 8 and of order 21.
1. Compute the unit-pulse response h[n] for n=0, 1, 2 for the discrete time system
y[n+2] + 1/2y[n+1] + 1/4y[n] = x[n+1] - x[n]
2. Determine if each of the following signals is periodic. If a signal is periodic, what is its period?
x[n] = 3sin(100n)
x[n] = 4cos(1.5πn)
3. For the discrete signals defined as the
Let K={k1,....km} be a conjugacy class in the finite group G.
a) Prove that the element K=k1+k2+....km is the center of the group ring R[G]
(check that g^-1Kg=K for all gin G)
b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. Prove that an el
A) Let G be a group of order 203. Prove that if H is normal subgroup of order 7 in G then H<=Z(G). Deduce that G is abelian in this case.
b)Let P be a normal Sylow p-subgroup of G and let H be any subgroup of G. Prove that P intersect H is the unique Sylow p-subgroup of H.
c)Let P be in Syl_p(G) and assume N is a normal su
A) Show that if n is odd then the set of all n-cycles consists of two conjugacy classes of equal size in An
b) Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for all a in A. (Such an element g is called a fixed point free automorphism)
c
