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Aut(Zn)|| Automorphism of finite cyclic Groups|| Aut(Z6)

Automorphism of infinite cyclic Groups|| Automorphism of Z

InnG=~G/Z(G)|| InnG is isomorphic to G/Z(G) with important applications and short tricks

Fundamental theorem of homomorphism|| Homomorphism || G/k~ G'|| Isomorphism

Inn G is a normal subgroup of Aut G|| Inner automorphism|| Automorphism

Automorphism || Innner automorphism|| InnG || InnG is a group

Isomorphism in group theory| Examples of isomorphism| Short tricks on isomorphism|MCQ on isomorphism

Simple Group MCQ

Wish you all a very happy and prosperous new year 🎊🎊

Group Homomorphism|| Kernal of homomorphism|| Important short tricks and results|| MCQ

Z4 w.r.t multiplication modulo 4 is not a group

Zm×Zn Group|| order of elements|| Is Zm×Zn cyclic|| Important results|| Short tricks|| MCQ

Multiplication of cycles in permutation group

Permutation| Cyclic permutation||Multiplication of cycles | Transposition|| Even and odd permutation

Un group || tricks to check cyclic or not|| Order of elements of Un group|| Subgroups of Un group

U(n) group|| Examples of Un group||Group of units || order of U(n) group || Is Un cyclic? || Unit

Group theory MCQ || Order of elements|| abelian groups || short tricks

K4 group|| order of elements|| order of subgroups|| Number of subgroups|| Normal subgroups||examples

Group theory MCQ || Order of ab || order of elements|| short tricks on order of elements

Q8 group||Quaternion Group|Order of elements|Subgroups of Q8 group||Order of subgroups||Centre of Q8

Mcq on subgroups|| order of group||Abelian group

#primeordergroup #simplegroup #abstractalgebra #subgroup #lagrangetheorem

Example of one step subgroup test

Simple Group|| Hamiltonian Group|| Short tricks||Mcqs