2019 Spring Algebra
Problem 1.
Does the symmetric group
(a) The dihedral group
(b) The quaternion group
Proof.
Problem 2.
Supppose
Proof.
Problem 3.
For a group
(Recall that if
Proof.
Problem 4.
Throughout this question we assume that
(a) Let
(b) Recall that
is an ideal of
(i)
(ii) Every element of
(iii)
Proof.
Problem 5.
Recall that the ring
(a) Prove that for every ideal
(b) Identify what is
Proof.
Problem 6.
Assume
Proof.
Problem 7.
Calculate the number of primitive elements of
Proof.
Problem 8.
Let
Proof.
Problem 9.
Let
Proof.
Problem 10.
Consider
(i)
(ii)
(iii)
Prove the following:
(a) If
(b) If