Yes, as shown by this example:
S={*}
G=(S,*)
*:S X S-->S
*(*,*)=*
However, I could not find any nontrivial examples.
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.
An operation that tells how many are in each group is division. Division breaks a total quantity into equal parts, indicating how many items are in each group when the total is split. For example, if you have 12 apples and divide them into 3 equal groups, each group would contain 4 apples.
The order of an element in a multiplicative group is the power to which it must be raised to get the identity element.
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.
Yes, that is part of the definition of a group.
Amines contain a nitrogen atom bonded to one or more carbon atoms, while aldehydes contain a carbonyl group and alcohols contain a hydroxyl group. Nitrogen is the element found in amines that is not present in aldehydes and alcohols.
Group 12 of the periodic table contain mercury (Hg).
Transition Metals group 3 to group 12 elements
I believe it is because 0 does not have an inverse element.
halogens & noble gases
The Sulfates mineral group typically contains one or several metallic elements
The s-block contains group 1-2.
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
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.
Acrylic materials contain Acrylyol group of Acrylic Acid (CH2=CH-COOH)
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.
The group 1 of the periodic table of Mendeleev (alkali metals) contain: lithium, sodium, potassium, rubidium, caesium and francium.