Review in Abstract Algebra

  Using a Cayley Table, how can we identify if a group is Abelian?

• a.     If there are no duplication of elements in all rows and columns.

• b. If the group order is even.

• c.   If the elements in the table are symmetric with respect to the main diagonal.

  If H is a subgroup of G, then the number of elements in H must be a factor of the number of elements in G.

• True

• False

How do we call a group with only one element?

• a. Identity Group

• b. Cyclic Group

• c. Subgroup

• d. Trivial Group

  Which is not a characteristics of a Klein-4 Group?

• a. It is an Abelian group

• b. It is a Cyclic group

• c.   The inverse of each element is itself

• d. The product of two elements is the other non-identity element

  In the Dihedral Group D₈ , every rotation is how many degrees?

• a. 45 degrees

• b. 60 degrees

• c. 90 degrees

• d. 120 degrees

The group Z₃ x Z₄ is cyclic.

• True

• False

   Number of elements in alternating group of degree 6 is

• a. 1440

• b. 720

• c. 360

• d. 120

Every finite cyclic group contains an element of every order that divides the order of the group.

• True

• False

  a * H = H * a relation holds if __________

• a. H is semigroup of an abelian group

• b. H is monoid of a group

• c. H is a cyclic group

• d. H is subgroup of an abelian group

We can say that H is normal when the subgroup H = {(1), (1, 2)} of S3.

• True

• False