Affine groupIn mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that the image of every line is a line. Over any field, the affine group may be viewed as a matrix group in a natural way. If the associated field of scalars the real or complex field, then the affine group is a Lie group.
PhenolsIn organic chemistry, phenols, sometimes called phenolics, are a class of chemical compounds consisting of one or more hydroxyl groups (−OH) bonded directly to an aromatic hydrocarbon group. The simplest is phenol, C6H5OH. Phenolic compounds are classified as simple phenols or polyphenols based on the number of phenol units in the molecule. Phenols are both synthesized industrially and produced by plants and microorganisms. Phenols are more acidic than typical alcohols.
Diazonium compoundDiazonium compounds or diazonium salts are a group of organic compounds sharing a common functional group where R can be any organic group, such as an alkyl or an aryl, and X is an inorganic or organic anion, such as a halide. According to X-ray crystallography the linkage is linear in typical diazonium salts. The bond distance in benzenediazonium tetrafluoroborate is 1.083(3) Å, which is almost identical to that for dinitrogen molecule (N≡N). The linear free energy constants σm and σp indicate that the diazonium group is strongly electron-withdrawing.
Trivial groupIn mathematics, a trivial group or zero group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: or depending on the context. If the group operation is denoted then it is defined by The similarly defined is also a group since its only element is its own inverse, and is hence the same as the trivial group.
Propylene oxidePropylene oxide is an acutely toxic and carcinogenic organic compound with the molecular formula CH3CHCH2O. This colourless volatile liquid with an odour similar to ether, is produced on a large scale industrially. Its major application is its use for the production of polyether polyols for use in making polyurethane plastics. It is a chiral epoxide, although it is commonly used as a racemic mixture. This compound is sometimes called 1,2-propylene oxide to distinguish it from its isomer 1,3-propylene oxide, better known as oxetane.
