BSc Practical Flashcard

Front

Let G denote the set of all n x n non-singular matrices with rational numbers as entries. What type of group is G under multiplication?

Back

G is an infinite, non-abelian group.

Front

What is the number of generators of the cyclic group G of order 8?

Back

The number of generators is 4.

Front

If (G,.) is a group such that (ab)^-1 =(a^-1)(b^-1) for all a, b in G, what type of group is G?

Back

G is an abelian group.

Front

What is the classification of the set {1,i,-i,-1}?

Back

It is a cyclic group.

Front

The set of integers Z forms a group under which operation?

Back

Z forms a group under the operation *(a, b)=a+b+2.

Front

Define a non-singular matrix.

Back

A non-singular matrix is a square matrix that has an inverse, meaning its determinant is not zero.

Front

What is a cyclic group?

Back

A cyclic group is a group that can be generated by a single element.

Front

What is an abelian group?

Back

An abelian group is a group in which the group operation is commutative, meaning a*b = b*a for all a, b in the group.

Front

What is a semigroup?

Back

A semigroup is a set equipped with an associative binary operation.

Front

What is the significance of the identity element in a group?

Back

The identity element is an element that, when combined with any element of the group, leaves that element unchanged.