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The case of the 105th cyclotomic polynomial is interesting because 105 is the least positive integer that is the product of three distinct odd prime numbers (3×5×7) and this polynomial is the first one that has a coefficient other than 1, 0, or −1: [3]
A cubic field K is called a cyclic cubic field if it contains all three roots of its generating polynomial f. Equivalently, K is a cyclic cubic field if it is a Galois extension of Q, in which case its Galois group over Q is cyclic of order three. This can only happen if K is totally real.
A cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring.
A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g 2, ... , g n−1}, where e is the identity element and g i = g j whenever i ≡ j (mod n); in particular g n = g 0 = e, and g −1 = g n−1.
Bicyclic molecules are described by IUPAC nomenclature. [6] [7] [8] The root of the compound name depends on the total number of atoms in all rings together, possibly followed by a suffix denoting the functional group with the highest priority.
For finite groups, an equivalent definition is that a solvable group is a group with a composition series all of whose factors are cyclic groups of prime order. This is equivalent because a finite group has finite composition length, and every simple abelian group is cyclic of prime order.
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
In organic chemistry, cheletropic reactions, also known as chelotropic reactions, [2] are a type of pericyclic reaction (a chemical reaction that involves a transition state with a cyclic array of atoms and an associated cyclic array of interacting orbitals). [1] Specifically, cheletropic reactions are a subclass of cycloadditions.