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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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∙ 2010-09-16 21:06:35
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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.
If X is an element in Group 2A and Y is an element in Group 7A what would be correct about the compound that would form between X and Y?
They would form an ionic compound.
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 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 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 an element determine by?
The identity of an element is determined by the number of protons.
Which subatomic element is responsible for identity of element?
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.
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.
What subatomic particle number determines the identity of an element?
The number of protons, which is the atomic number of an element, determines the identity of an element.
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.
What are the properties of mathematical system to be a commutative group?
Closure, an identity element, inverse elements, associative property, commutative property
