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If you mean in the group {1, -1, i, -i, j, -j, k, -k}, the identity element is 1.

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Q: What is the identity element of the quaternion group?

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The property of multiplicative identity, i, of a set S is an element, is that for every element x in S,x * i = x = i * x

Assuming that the question is in the context of the operation "addition", The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set. There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.

The identity property for a set states that there exists an element in the set, denoted by 0, such that for all members, x, of the set,x + 0 = 0 + x = x.

In abstract algebra, the properties of a group G under a certain operation are:Associativity: (ab)c = a(bc) for all a, b and c belonging to GIdentity: Identity e belongs to G.Inverse: If ab = ba = a, where a is the identity, then b is the inverse of a.

They would form an ionic compound.

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The order of an element in a multiplicative group is the power to which it must be raised to get the identity element.

In a group, the identity property is that each group contains an element, i, such that for all elements x, in the group, i*x = x*i = x. i is called the identity element.

0, zero, is defined as the identity element for addition and subtraction. * * * * * While 0 is certainly the identity element with respect to addition, there is no identity element for subtraction. The identity element of a set, for a given operation, must commute with every element of the set. Since a - 0 ≠ 0 - a, according to group theory, 0 is not an identity with respect to subtraction.

There is no such thing as an "identity of element". The identity element of multiplication, on the other hand, is the number 1.

An identity element is an element of a set which leaves other elements unchanged when combined with them. For multiplication, the identity element is 1 .

The properties of a subgroup would include the identity of the subgroup being the identity of the group and the inverse of an element of the subgroup would be the same in the group. The intersection of two subgroups would be a separate group in the system.

The identity of an element is determined by the number of protons.

There is no individual sub-atomic particle that is responsible for the identity of an element. It is the way the electrons, protons and (neutrons) are arranged in an element that gives it it's identity.

An Identity element in multiplication is one that when you multiply a value by the identity element, that the original value is returned. The only identity element in multiplication is 1. If you multiply any value (other than infinity which is a special case of mathematics), the value returned will be 0. The identity element for addition is 0.

The number of protons, which is the atomic number of an element, determines the identity of an element.

It depends, but all groups are 2 or more. * * * * * That may be true elsewhere but in the special context of Group theory, you can have a group consisting of only one element - the identity.

Closure, an identity element, inverse elements, associative property, commutative property

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