group

1 . The intersection of two subgroups K and H of G is always:

• A subgroup

• A subgroup only if HK=KH

• Never a subgroup

The union of two subgroups H and K of G is a subgroup only if:

• H and K are disjointed

• One is contained in the other

• They have a same order

If a group has four element it is known as

• Finite group

• Infinite group

• Cyclic group

Which of the following group is a abelian?

• Group of two cross two mattresses under multiplication

• Set of real numbers under addition

• Group of permutations of 3 objective

The order of an element a in a group is defined as

• The position of a in the set

• 
• The total number of elements in the group

What is the identity element in a group?

• An element that is it own inverse

• An element that combines with any element to give that element back

• The largest element in the group

Which of the following is not a requirement for a set and operations to be considered a group?

• Associativity

• Commutativity

• Inverse elements

Associativity must hold for which of the following to be a group?

• Only the identity element

• All elements in the set

• Only elements with inverses

Which of the following operations is associative?

• Subtraction on integer

• Division on real numbers

• Addition on real numbers

Which of the following is true about all groups?

• They are commutative

• They have infinite element

• They are associative.