Challenge Yourself #CHAPTER3

a * H = H * a relation holds if __________.

H is semigroup of an abelian group.

H is monoid of a group.

H is a cyclic group.

H is subgroup of an abelian group.

A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called ____________.

Isomorphic

Homomorphic

Cyclic group

Heteromorphic

An isomorphism of a group onto itself is called ____________.

Homomorphism

Heteromorphism

Epimorphism

Automorphism

The homomorphism of a group onto itself is defined as the ___________.

Endomorphism

Homomorphism

Automorphism

Heteromorphism

The elements of a vector space form a/an ____________ under vector addition.

abelian group

Commutative group

Associative group

semigroup

A set of representatives of all the cosets is called _________.

Transitive

Reversal

Equivalent

Transversal

Which of the following statement is true?

The set of all matrices forms a group under multiplication.

The set of all rational negative numbers forms a group under multiplication.

The set of all non-singular matrices forms a group under multiplication.

The set of matrices forms a subgroup under multiplication.

How many different non-isomorphic Abelian groups of order 8 are there?

Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________.

does not form a group

does not have the right identity element

Forms a non-commutative group

Forms a group if the empty string is removed from

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