Extra Credit
If you missed any points on problems 2 or 3 of Homework 5, here's a chance to get some or all
of them back. If you lost x points on problems 2 and 3 of Homework 5 and you get a score of y%
on this extra credit assignment, I'll add xy/100 (rou
1. The RSA cipher, with public key n = 7822643 and encryption exponent e = 17, was used
to encrypt a message. The ciphertext is: 5785045 6445108 3550040 475858 5843081.
Determine the decryption exponent and the original plaintext message: We first must
fa
1. If f: G -> H is a homomorphism of groups, and if B is a normal subgroup of H, show that
f -1(B) is a normal subgroup of G.
Let g be an element of G, and x an element of f -1(B). Then f(gxg-1) = f(g)f(x)(f(g)-1 is in
B, since f(x) is in B and since B is
(10 points) Let G be a group acting on a set S. Show that the orbits form a partition of S; i.e., S
is the disjoint union of the orbits.
Answer: Let x be in orb G (s) and in orb G (s'). Then x = gs and x = g's' for some g and g' in G. But
this means that