Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
HalomethaneHalomethane compounds are derivatives of methane () with one or more of the hydrogen atoms replaced with halogen atoms (F, Cl, Br, or I). Halomethanes are both naturally occurring, especially in marine environments, and human-made, most notably as refrigerants, solvents, propellants, and fumigants. Many, including the chlorofluorocarbons, have attracted wide attention because they become active when exposed to ultraviolet light found at high altitudes and destroy the Earth's protective ozone layer.
TrihalomethaneIn chemistry, trihalomethanes (THMs) are chemical compounds in which three of the four hydrogen atoms of methane () are replaced by halogen atoms. Many trihalomethanes find uses in industry as solvents or refrigerants. THMs are also environmental pollutants, and many are considered carcinogenic. Trihalomethanes with all the same halogen atoms are called haloforms. Only chloroform has significant applications of the haloforms. In the predominant application, chloroform is required for the production of tetrafluoroethylene (TFE), precursor to teflon.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
HalideIn chemistry, a halide (rarely halogenide) is a binary chemical compound, of which one part is a halogen atom and the other part is an element or radical that is less electronegative (or more electropositive) than the halogen, to make a fluoride, chloride, bromide, iodide, astatide, or theoretically tennesside compound. The alkali metals combine directly with halogens under appropriate conditions forming halides of the general formula, MX (X = F, Cl, Br or I). Many salts are halides; the hal- syllable in halide and halite reflects this correlation.
Enantioselective synthesisEnantioselective synthesis, also called asymmetric synthesis, is a form of chemical synthesis. It is defined by IUPAC as "a chemical reaction (or reaction sequence) in which one or more new elements of chirality are formed in a substrate molecule and which produces the stereoisomeric (enantiomeric or diastereomeric) products in unequal amounts." Put more simply: it is the synthesis of a compound by a method that favors the formation of a specific enantiomer or diastereomer.
Transfer hydrogenationIn chemistry, transfer hydrogenation is a chemical reaction involving the addition of hydrogen to a compound from a source other than molecular . It is applied in laboratory and industrial organic synthesis to saturate organic compounds and reduce ketones to alcohols, and imines to amines. It avoids the need for high-pressure molecular used in conventional hydrogenation. Transfer hydrogenation usually occurs at mild temperature and pressure conditions using organic or organometallic catalysts, many of which are chiral, allowing efficient asymmetric synthesis.
InterhalogenIn chemistry, an interhalogen compound is a molecule which contains two or more different halogen atoms (fluorine, chlorine, bromine, iodine, or astatine) and no atoms of elements from any other group. Most interhalogen compounds known are binary (composed of only two distinct elements). Their formulae are generally , where n = 1, 3, 5 or 7, and X is the less electronegative of the two halogens. The value of n in interhalogens is always odd, because of the odd valence of halogens.
Substituted amphetamineSubstituted amphetamines are a class of compounds based upon the amphetamine structure; it includes all derivative compounds which are formed by replacing, or substituting, one or more hydrogen atoms in the amphetamine core structure with substituents. The compounds in this class span a variety of pharmacological subclasses, including stimulants, empathogens, and hallucinogens, among others.
Linear groupIn mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K). Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class.
