(1) Let G be a group and H, K be subgroups of G.
(a) Show that if H is a normal subgroup, then HK = {xy|x ? H, y ?
K} is a
subgroup of G.
(b) Show that if H and K are both normal subgroups, then HK is also
a normal
subgroup.
(c) Give an example of subgroups H and K such that HK is not a
subgroup of G.
Pass the signal x5 through the filter h using the command: x6 =
filter(h,1,x5); In your report, include a plot of the amplitude
spectrum of x6 (use the normalized frequency axis as you did for
previous parts of this project).
Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u)
x)) (λ(u) u)))))
zero: (λ(f) (λ(x) x))
one: (λ(f) (λ(x) (f x)))
two: (λ(f) (λ(x) (f (f x))))
three: (λ(f) (λ(x) (f (f (f x)))))
i. (4 pt) What is the result of (op one)?
ii. (4 pt) What is the result of (op two)?
iii. (4 pt)What is the result of (op three)?
iv. (3 pt) What computation does op perform?
The Golomb's sequence is G(n) = 1 + G(n - G(G(n -
1)))
For what n value (approximately) does your
computer stop producing output? Why is
this?
The following is my code, but I don't know what would be the max
value for n, since my computer stuck at 80
#include <iostream>
using namespace std;
int golombSequence(int);
int golombSequence(int
max){
if(max == 1){
return 1;
}
else{
return 1 + golombSequence(max -
golombSequence(golombSequence(max-1)));
}
}
int main(int argc,
const char...
Calculate delta H for the reaction H(g) + Br(g) = HBr(g), given
the following information:
H2(g) + Br2(g) = 2HBr(g) delta H = -72 kJ
H2(g) = 2H(g) delta H = +436 kJ
Br2(g)= 2Br(g) delta H = +224 kJ
4.- Show the solution:
a.- Let G be a group, H a subgroup of G and a∈G. Prove that the
coset aH has the same number of elements as H.
b.- Prove that if G is a finite group and a∈G, then |a| divides
|G|. Moreover, if |G| is prime then G is cyclic.
c.- Prove that every group is isomorphic to a group of
permutations.
SUBJECT: Abstract Algebra
(18,19,20)