CH 1 - Definition and Examples of Groups

Question 1

State the lemma on composition of functions.

Define a permutation of a set X.

Define the symmetric group.

Answer 1

Question 2

State the theorem on permutations and disjoint cycles.

State the theorem on permutations and transpositions.

Define General Linear Groups.

Answer 2

Question 3

Construct the Cayley Table for the Klein 4 Group.

Define the Quaternion Group.

Answer 3

Question 4

Define an isomorphism from G to H.

Answer 4

Question 5

Define the (finite and infinite) order of an element x.

State a result on the order of x versus a power of x.

Answer 5