Abelian Group Quiz

shich of the following is always true for an abelian group?

• a.be

• a.b-b.c

• a.a-e

• a.e=a²

An abelian group must be:

• associative but not neccessary commutative

• commutative and associative

• only commutative

• none of the above

The group (2,+ is:

• not a group

• A non-abelian group

• An abelian group

• abelian group

which of the following is not an abelian group?

• (R₁+

• (Q₁+

• (2+

• (Z+

If G is an abelian group, which of the following holds for all a,beG?

• (ab)²

• a²b²

• ab¹b¹c

• all of the above

In an abelian group G, the inverse of a.bis

• b¹a¹

• a-¹b-¹

• (a.b)-¹

• all of the above

which of the following is a necessary condition for a group to abelian?

• commutative

• Inverse of every element exists

• Associativity

• Identity exists

The group (2, X2₁+ is:

• non abelin

• not a group

• abelian

• Infinite

A finite group is Abelian if:

• every element is its own inverse

• The group has order 2

• The group

• Any of the above

The set of all 2x2 invertible matrices under multiplucation is:

• an abelian group

• A non abelian group

• Not a group

• cyclic group