Group extension
From Wikipedia, the free encyclopedia
In mathematics, for G a group, G′ is an extension of G if there is an exact sequence
This situation is sometimes described by saying that G′ is an extension of G by H.
In other words: G' is a group, G is a normal subgroup of G' and the quotient group G'/H is isomorphic to group H. In contexts where the extension nomenclature is used, G and H are known and the properties of G' are to be determined.
One extension, the direct product, is immediately obvious and several other general classes of extensions are known but no theory exists that treats all the possible extensions at one time and group extension is usually described as a "hard" problem.
