Commutator Subgroup & Theorem on Commutator Subgroup || A group G is solvable iff G(k) = (e) || M.Sc
Автор: Gouri Shankar (Maths)
Загружено: 2024-03-09
Просмотров: 8071
Commutator Subgroup & Theorem on Commutator Subgroup || A group G is solvable iff G(k) = (e) || M.Sc
Our target is learn a theorem : A group G is solvable iff G(k) = (e).
But before this above theoem we have to cover these theorem which is very very important to learn above theorem.
In this video if have covered topic
1. Commutator Subgroup
2. Theorem based on Commutator Subgroup
Theorem : If G' is commutator subgroup of G. Then
(i) G' is normal in G.
(ii) G/G' is abelian.
Theorem : If N is any normal subgroup of G such that G/N is abelian. Then definately Commutator subgroup G' will contain in normal subgroup N. i.e., N is Super Set of Commutator subgroup G'.
Theorem : If any subgroup H of G containing Commutator subgroup G'. Then definately H will be a normal subgroup of G.
More video Lectures For M.Sc (Mathematics) ~ Modern Abstract Algebra
(1) First Law of Isomorphism/Fundamental Theorem on Homomorphis
• First Law Of Isomorphism OR Fundamental Th...
(2) Second Law of Isomorphism
• Second Law of Isomorphism Theorem || B.Sc/...
(3) Jordan Holder Theorem
• Jordan Holder Theorem (Complete Proof) || ...
(4) Solvable Group and Solvable series and their conditions
• Definition of Solvable Group || Solvable S...
(5) Every subgroup of a solvable group is solvable
• Every subgroup of a solvable group is solv...
(6) Upper Central Series, Lower Central Series and Nilpotent Group
• Upper Central Series, Lower Central Series...
Доступные форматы для скачивания:
Скачать видео mp4
-
Информация по загрузке:
![Катастрофа, которая нас (возможно) ждёт [Veritasium]](https://ricktube.ru/thumbnail/NKeIqEou5k8/mqdefault.jpg)
