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For example, in the symmetric group shown above, where ord(S 3) = 6, the possible orders of the elements are 1, 2, 3 or 6. The following partial converse is true for finite groups: if d divides the order of a group G and d is a prime number, then there exists an element of order d in G (this is sometimes called Cauchy's theorem).
In organic chemistry, a functional group is a substituent or moiety in a molecule that causes the molecule's characteristic chemical reactions.The same functional group will undergo the same or similar chemical reactions regardless of the rest of the molecule's composition.
For example, it is commonly asserted that the reactivity of alkali metals (Na, K, etc.) increases down the group in the periodic table, or that hydrogen's reactivity is evidenced by its reaction with oxygen. In fact, the rate of reaction of alkali metals (as evidenced by their reaction with water for example) is a function not only of position ...
For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it; in particular, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. A group action on a vector space is called a representation of the
In this type of substitution reaction, one group of the substrate participates initially in the reaction and thereby affects the reaction. A classic example of NGP is the reaction of a sulfur or nitrogen mustard with a nucleophile, the rate of reaction is much higher for the sulfur mustard and a nucleophile than it would be for a primary or secondary alkyl chloride without a heteroatom.
Another example of a double displacement reaction is the reaction of lead(II) nitrate with potassium iodide to form lead(II) iodide and potassium nitrate: + + Forward and backward reactions According to Le Chatelier's Principle , reactions may proceed in the forward or reverse direction until they end or reach equilibrium .
The reaction order is 1 with respect to B and −1 with respect to A. Reactant A inhibits the reaction at all concentrations. The following reactions follow a Langmuir–Hinshelwood mechanism: [4] 2 CO + O 2 → 2 CO 2 on a platinum catalyst. CO + 2H 2 → CH 3 OH on a ZnO catalyst. C 2 H 4 + H 2 → C 2 H 6 on a copper catalyst. N 2 O + H 2 ...
In organic chemistry, a group transfer reaction is a class of the pericyclic reaction where one or more groups of atoms is transferred from one molecule to another. Group transfer reactions can sometimes be difficult to identify when separate reactant molecules combine into a single product molecule (like in the ene reaction).