In mathematics, for G a group or algebra over a field, or other algebraic structure, G′ is an extension of G if there is an exact sequence

$0\backslash rightarrow\; H\backslash rightarrow\; G\text{'}\backslash rightarrow\; G\backslash rightarrow\; 0.$

This situation is sometimes described by saying that G′ is an extension of G by H.

See also

• Central extension
• Extension problem
• Field extension

Abstract algebra | Group theory