In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence
If G is an extension of Q by N, then G is a group, N is a normal subgroup of G and the quotient group G/N is isomorphic to group Q. Group extensions arise in the context of the extension problem, where the groups Q and N are known and the properties of G are to be determined.
An extension is called a central extension if the subgroup N lies in the center of G.
Read more about Group Extension: Extensions in General, Central Extension
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“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
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