lec#72(4) Closets and normal subgroups of Quaternion groups

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In this video we will learn
Set of Quaternion full applying full group theory
composition table, orders, possible subgroups, derived/commotator subgroups, center, , conjugacy classes, left/right closets, normal subgroups, normalizer, centralizer wit

Here you can find all topics of group theory :
Introduction to Algebra linear abstract algebra cayley table residue class unit modulo n nth roots of unity properties of group Order of group and order of element Order subgroup Three step subgroup testTwo step subgroup test One step subgroup test finite subgroup test Results on subgroup Abelian group theorem cyclic group cyclic subgroup how to find order of an element number of elements of each order in a cyclic Generator of finite and infinite cyclic group euler function number of generators of finite cyclic Under what condition U(n) is cyclic group theorems about cyclic group cosets coset define lagrange's homomorphism examples isomorphism number of non isomorphic group non isomorphic groupHomomorphism monomorphism epimorphism isomorphism endomorphism Automorphism Inner Automorphism examples center of a group Examples on Center centralizer Normalizer Normal subgroup theorem conjugacy class factor group commutator group metabelian perfect moderate solvable group characteristic group Cauchy Sylow 1st Sylow 2nd result sylow 3rd theorem sylow's theorems permutation Product of permutation symmetric group circular permutation circular permutation properties transposition even and odd permutation Alternating group Integral power of permutation Inversion cayley's theorem Permutation theorem results properties with full detail and explanation basic concepts short mcqs tricks
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