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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.
Which element is not found in the carboxylic acid functional group?
The carboxylic acid functional group always contains carbon (C), oxygen (O), and a hydroxyl group (-OH). It does not contain hydrogen (H) as a separate element, but hydrogen is present within the functional group attached to the carbon atom.
What is element H on the periodic table?
The element 'H' is hydrogen, and is NO. 1 in the Periodic Table.
How Order of element is equal to its inverse in group?
The order of an elementg in a group is the least positive integer k such that gk is the identity.Now look at the same group, we know there exists an element h such that gh=hg=e where e is the identity. This must be true because existence of inverses is one of the conditions required for a set to be a group. So if gk=e and gh=e, then gk =gh and we see the relation between k, the order and h the inverse in the group.
G is finite where the number of subgroups in g is finite?
Actually a stronger statement can be made:A group G is finite if and only if the number of its subgroups is finiteLet G be a group. If G is finite there is only a finite number of subsets of G, so clearlya finite number of subgroups.Now suppose G is infinite , let'ssuppose one element has infinite order. The this element generates an infinite cyclicgroup which in turn contains infinitely many subgroups.Now suppose all the subgroups have finite order Take some element of G and let it generate a finite group H. Now take another element of G not in H and let it generate a finite group I. Keep doing this by next picking an element of G not H or I. You can continue this way.
What is the element group called carbonate?
"Carbonate" is not an element or an element group; instead, it is a polyatomic anion and is one of a large group of oxyanions.
Which element is smallest in size?
This element is hydrogen (H).
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.
Is beryllium a pure substance or a mixture?
Compound, no group 2 or group 1 (except H if its considered) exist in elemental form naturally.
What is hydrogens element name?
Hydrogen is a chemical element with the symbol H and atomic number 1.
What is the group number of the element Cadmium?
The element "Cadmium" is in group number 12.
Which element is the first element in group 1?
If we look at the periodic table, we can see that the first element in Group I is Hydrogen.
