split extension - translation to russian
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split extension - translation to russian

GROUP FOR WHICH A GIVEN GROUP IS A NORMAL SUBGROUP
Extension problem; Extension (algebra); Split extension; Extension of a group; Central extension (mathematics)
  • Figure 1

split extension         

математика

расщепляемое расширение

extension problem         

математика

задача продолжения

group extension         

математика

расширение группы

Definition

split pea
¦ noun a pea dried and split in half for cooking.

Wikipedia

Group extension

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 {\displaystyle Q} and N {\displaystyle N} are two groups, then G {\displaystyle G} is an extension of Q {\displaystyle Q} by N {\displaystyle N} if there is a short exact sequence

1 N ι G π Q 1. {\displaystyle 1\to N\;{\overset {\iota }{\to }}\;G\;{\overset {\pi }{\to }}\;Q\to 1.}

If G {\displaystyle G} is an extension of Q {\displaystyle Q} by N {\displaystyle N} , then G {\displaystyle G} is a group, ι ( N ) {\displaystyle \iota (N)} is a normal subgroup of G {\displaystyle G} and the quotient group G / ι ( N ) {\displaystyle G/\iota (N)} is isomorphic to the group Q {\displaystyle Q} . Group extensions arise in the context of the extension problem, where the groups Q {\displaystyle Q} and N {\displaystyle N} are known and the properties of G {\displaystyle G} are to be determined. Note that the phrasing " G {\displaystyle G} is an extension of N {\displaystyle N} by Q {\displaystyle Q} " is also used by some.

Since any finite group G {\displaystyle G} possesses a maximal normal subgroup N {\displaystyle N} with simple factor group G / N {\displaystyle G/N} , all finite groups may be constructed as a series of extensions with finite simple groups. This fact was a motivation for completing the classification of finite simple groups.

An extension is called a central extension if the subgroup N {\displaystyle N} lies in the center of G {\displaystyle G} .

What is the Russian for split extension? Translation of &#39split extension&#39 to Russian