Abstract Algebra Session 2 Refresher

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

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

• If the group order is even.

• 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.

• Always True

• Always False

• Sometimes True

• Sometimes False

The following are POSSIBLE subgroup orders of G with order 12 except:

• 3

• 4

• 5

• 6

How can we know if a group is cyclic?

• A group G is cyclic if and only if all its elements can generate G.

• A group G is cyclic if and only if at least one of its elements can generate G.

How do we call a group with only one element?

• Identity Group

• Cyclic Group

• Subgroup

• Trivial Group

Which of the statements is true?

• All Abelian Groups are Cyclic.

• All Cyclic Groups are Abelian.

What is an element of the group which can generate the rest of the elements of the group considering the properties that a group must satisfy?

• Identitiy Element

• Group Generator

• Inverse Element

• 1

• 2

• 3

• 4

Tags

CCSS.HSF-IF.C.8B

• 3

• 2

• 1

• 0

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

• It is an Abelian Group.

• It is a Cyclic Group.

• The inverse of each element is itself.

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