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Group theory

Quiz by Brindha PSGRKCW (Maths-SF)

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10 questions
Show answers
  • Q1
    Which property does the inverse of an element in a group satisfy?
    It leaves other group elements unchanged.
    It transforms the other group elements into inverses.
    It swaps the other group elements.
    It is the element that, when combined with the original element, produces the identity element.
    It generates the cyclic subgroup.
    30s
  • Q2
    What is the closure property in group theory?
    It states that the result of combining any two elements in a group is also an element of the group.
    It states that every element in a group is associated with a unique inverse.
    It states that every element in a group has an inverse.
    It states that the product of any two elements in a group is commutative.
    It states that every group has a distinct identity element.
    30s
  • Q3
    What is an abelian group?
    A group in which the group operation is commutative.
    A group with no inverse elements.
    A group with no identity element.
    A group with non-commutative operations.
    A group with non-associative operations.
    30s
  • Q4
    In group theory, what is the order of a group?
    The number of distinct operations in the group.
    The number of subgroups in the group.
    The number of permutations in the group.
    The number of elements in the group.
    The number of generators of the group.
    30s
  • Q5
    What is a subgroup in group theory?
    A group that is not closed under the group operation.
    A group that has a different group operation than the original group.
    A group that contains all the elements of the original group.
    A subset of a group that is itself a group under the same group operation.
    A group consisting of only the identity element.
    30s
  • Q6
    What is the Lagrange's theorem in group theory?
    It states that the composition of any two elements always results in a unique element.
    It states that the group operation is commutative for all elements.
    It states that every group has a distinct identity element.
    It states that the order of a subgroup divides the order of the group.
    It states that every element in a group has an inverse.
    30s
  • Q7
    What is the definition of a group in group theory?
    A set equipped with a unary operation.
    A set equipped with multiple binary operations.
    A set equipped with no operations.
    A set equipped with a binary operation that satisfies closure, associativity, identity, and inverse properties.
    A set equipped with a ternary operation.
    30s
  • Q8
    What is the inverse element in a group?
    An element that is not part of the group
    An element that is the largest in the group
    An element that is equal to the identity element
    An element that cancels out another element when combined
    30s
  • Q9
    What is a cyclic group?
    A group generated by a single element
    A group with an infinite number of elements
    A group that is not associative
    A group with no inverse elements
    30s
  • Q10
    What is a normal subgroup in group theory?
    A subgroup that is not closed under multiplication
    A subgroup that does not contain the identity element
    A subgroup that is invariant under conjugation by any element in the group
    A subgroup that is larger than the main group
    30s

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