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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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What is a multiplicative identity property?

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


Give two reason for the set of odd integers is not a group?

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.


What is identity property of addition?

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.


What are the properties of a group?

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.


What is the order of an element of a group?

The order of a group is the same as its cardinality - i.e. the number of elements the set contains. The order of a particular element is the order of the (cyclic) group generated by that element - i.e. the order of the group {...a-4, a-3, a-2, a-1, e, a, a2, a3, a4...}. If these powers do not go on forever, it will have a finite order; otherwise the order will be infinite.

Related questions

What is the order of an element in a group?

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


What is an identify propery?

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.


What is the identity element for addition and subtraction?

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.


What are the properties of a subgroup?

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.


What is the identity of element of multiplication?

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


What is the identity element for multiplication?

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 .


What is the identity of an element determine by?

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


How many are in a group?

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.


Prove that the set of all real no is a group with respect of multiplication?

There are four requirements that need to be satisfied: A. Closure: For any two elements of the group, a and b, the operation a*b is also a member of the group. B. Associativity: For any three members of the group, a*(b*c) = (a*b)*c C. Identity: There exists an element in the group, called the identity and denoted by i, such that a*i = i*a for all a in the group. For real numbers with multiplication, this element is 1. D. Inverse: For any member of the group, a, there exists a member of the group, b, such that a*b = b*a = 1 (the identity). b is called the inverse of a and denoted by a-1.


What are the properties of mathematical system to be a commutative group?

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


Why is 0 not a identity element for multiplication?

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.


How do you find proper subgroups of a cyclic group of order 6?

A cyclic group of order 6 is isomorphic to that generated by elements a and b where a2 = 1, b3 = 1, or to the group generated by c where c6 = 1. So, find the identity element, 1. Next find an element which when operated on by itself, equals the identity. This element will correspond to a or c3. Finally find an element which when operated on by itself twice (so that it is cubed or multiplied by 3), equals the identity. This element will correspond to b or c2. The subgroups {1}, (1, a} = {1, c3} and {1, b, b2} = {1, c2, c4} will be proper subgroups.