Mid Term: Abstract Algebra

A trivial subgroup consists of ___________

• Identity element
• Coset
• Inverse element
• Ring

Minimum subgroup of a group is called _____________

• a commutative subgroup
• a lattice
• a trivial group
• a monoid

__________ is not necessarily a property of a Group.

• Commutativity
• Existence of inverse for every element
• Existence of Identity
• Associativity

A group of rational numbers is an example of __________

• a subgroup of a group of integers
• a subgroup of a group of real numbers
• a subgroup of a group of irrational numbers
• a subgroup of a group of complex numbers

Intersection of subgroups is a ___________

• group
• subgroup
• semigroup
• cyclic group

The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

• 2
• 3
• 1
• 4

What is a circle group?

• a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements
• a subgroup rational numbers having magnitude 2 of the group of real elements
• a subgroup irrational numbers having magnitude 2 of the group of nonzero complex elements
• a subgroup complex numbers having magnitude 1 of the group of whole numbers

The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

• 2
• 3
• 1
• 4

A non empty set A is termed as an algebraic structure ________

• with respect to binary operation *
• with respect to ternary operation ?
• with respect to binary operation +
• with respect to unary operation –

A group (M,*) is said to be abelian if ___________

• (x+y)=(y+x)
• (x*y)=(y*x)
• (x+y)=x
• (y*x)=(x+y)