L-17 || Normal subgroup of a group || simple group || group theory || bsc msc mathematics

#mscmath #bsc #algebra #group
Normal subgroup definition, Simple group
Group theory in mathematics for BSc and MSc students. Here you can watch videos of all theorems and examples.
#bsc #bscmaths #msc #mscmathematics #kuk #mdu #cdlusirsa #ptu
🧡➕➖✖➗➕➖✖➗➕➖✖➗➕➖✖➗🧡
Group theory is the study of a set of elements present in a group, in Maths. A group’s concept is fundamental to abstract algebra. Other familiar algebraic structures namely rings, fields, and vector spaces can be recognized as groups provided with additional operations and axioms. The concepts and hypotheses of Groups repeat throughout mathematics. Also, the rules of group theory have influenced several components of algebra.
1. Group and subgroups
2. Cosets
3. Homomorphisms and Automorphisms
4. Permutation Group
5. Ring and Fields
6. Ideal and Quotient Rings
7. Homomorphisms of Rings
8. Euclidean Rings
9. Polynomial Rings
🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧
Msc mathematics bsc mathematics algebra with proof of theorems.
#mscmath #bsc #algebra #group
Group theory in mathematics for BSc and MSc students. Here you can watch videos of all theorems and examples.
#bsc #bscmaths #msc #mscmathematics #kuk #mdu #cdlusirsa #ptu
Group theory is the study of a set of elements present in a group, in Maths. A group’s concept is fundamental to abstract algebra. Other familiar algebraic structures namely rings, fields, and vector spaces can be recognized as groups provided with additional operations and axioms. The concepts and hypotheses of Groups repeat throughout mathematics. Also, the rules of group theory have influenced several components of algebra.
Groups:
Elementary concepts (homomorphism, subgroup, coset,normal subgroup, simple group). Solvable groups, commutator subgroup,Sylow theorems, structure of finitely generated Abelian groups. Symmetric,alternating,dihedral ,and general linear groups.
Rings:
Commutative rings and ideals (principal,prime,maximal). Chinese remainder theorem. Integral domains, factorization,principal ideal domains,Euclidean domains,polynomial rings,Gauss Lemma,Eisenstein’s irreducibility criterion.
Modules:
Elementary concepts: homomorphism, linear independence,exactsequence, finite presentation, torsion. Structure of finitely generated module so vera principal ideal domain.
Fields:
Extensions: finite,algebraic, separable, inseparable, transcendental, splitting field of apolynomial, primitive element theorem, algebraic closure. Finite Galois extensions and the Galois correspondence between subgroups of the Galois group and sub extensions. Solvable Galois groups and the problem of expressing the roots of a polynomial in terms of radicals. Finite fields.
Related content you can found