0
Yes, as shown by this example:
S={*}
G=(S,*)
*:S X S-->S
*(*,*)=*
However, I could not find any nontrivial examples.
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∙ 12y ago
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What is the no of generator in n order group?
In abstract algebra, a generating set of a group is a subset of that group. In that subset, every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.
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 subgroup in mathematics?
In mathematics, a subgroup H of a group G is a subset of G which is also a group with respect to the same group operation * defined on G. H contains the identity element of G, is closed with respect to *, and all elements of H have their inverses in H as well.
What is inverse in algebra?
Given a set and a binary operation defined on the set, the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation. If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k. If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.
Does a group have to be closed under its operation?
Yes, that is part of the definition of a group.
What groups of element does the d-block contain?
Transition Metals group 3 to group 12 elements
Which group contains an element at is liq at STP?
Group 12 of the periodic table contain mercury (Hg).
Why are the rational numbers under the operation of multiplication not a group?
I believe it is because 0 does not have an inverse element.
What group of elements does the p block on the periodic table contain?
halogens & noble gases
What element do amines contain that aldehydes and alcohol do not?
It is Nitrogen, located in the amino-group ( -NH2)
What group of element does the d block contain?
Transition Metals group 3 to group 12 elements
What groups of element does the s-block contain?
The s-block contains group 1-2.
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
Does carbon contain acid groups?
Carbon is an element, and doesn't contain anything but carbon. An acid-group is comprised from carbon, hydrogen and oxygen.
What do you call a name for a number that contains at least one of the operation?
A number does not contain an operation.A number does not contain an operation.A number does not contain an operation.A number does not contain an operation.
What is element in acrylic?
Acrylic materials contain Acrylyol group of Acrylic Acid (CH2=CH-COOH)
What is the no of generator in n order group?
In abstract algebra, a generating set of a group is a subset of that group. In that subset, every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.
