A) An even number in the group. B) An element that is the largest in the group. C) An element that is the smallest in the group. D) An element in the group such that when combined with any other element, the result is that other element.
A) For all elements a, b, c in the group, (a + b) * c = a * (b * c). B) For all elements a, b, c in the group, (a * b) * c = a * (b * c). C) For all elements a, b in the group, a * b = b * a. D) For all elements a, b in the group, a = a * b.
A) In a finite group, the order of a subgroup divides the order of the group. B) A theorem about linear algebra. C) The sum of all elements in a group equals zero. D) The largest element in a group.
A) A group with only one element. B) A group where the group operation is commutative. C) A group with no identity element. D) A group where the operation is defined only for odd numbers.
A) A group with no identity element. B) A group with no operation defined. C) A group generated by a single element. D) A group where elements can have multiple inverses.
A) The sum of all elements in a group. B) The set of inverses of the group. C) The largest element in the group. D) The set of elements that commute with every element of the group.
A) The smallest element in the group. B) The sum of all elements in the group. C) The largest element in the group. D) The number of elements in the group.
A) A function between two groups that preserves the group structure. B) The largest element in the group. C) The sum of all elements in a group. D) The smallest element in the group.
A) The sum of all elements in a group is the same. B) The groups have the same structure, even if the elements may be labeled differently. C) The smallest element in the groups is the same. D) The largest element in the group is identical.
A) A group of integers. B) A group where the elements are permutations of a set and the group operation is composition of permutations. C) A group with only one element. D) A group with no identity element.
A) A group with only one element. B) A group of integers. C) A group with no identity element. D) The group of symmetries of a regular polygon.
A) A group of integers. B) A group with no identity element. C) A group with only one element. D) The group of all permutations of a set.
A) A group with no identity element. B) The subgroup of the symmetric group consisting of even permutations. C) A group with only one element. D) A group of integers.
A) The sum of all elements in a group. B) A theorem about linear algebra. C) Every group is isomorphic to a permutation group. D) The largest element in a group.
A) A group of integers. B) A set of elements that are all conjugates of each other. C) A group with only one element. D) A group with no identity element.
A) A group with only one element. B) A group with no identity element. C) A group of integers. D) An isomorphism from a group to itself.
A) The sum of all elements in a group. B) The subgroup generated by all commutators. C) The largest element in the group. D) A group with no identity element.
A) The group of cosets of a normal subgroup. B) The largest element in the group. C) The sum of all elements in a group. D) A group with no identity element. |