order of element is a divisor of order of group

Normal subgroup|important theorems

Order of an element divides order of the group | order of a group and order of an element | cosets

Order of every element of a finite group is finite and less than or equal to order of the group

Every subgroup of a cyclic group is cyclic.

(Corollary:2) The order of every element of a finite group is divisor of the order of the group.

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Let G be group, a ɛ G and O(a)=n. Then for any positive integer k, O(a^k) =n/(n,k).

O(HK)=o(H)o(K)/o(intersection of H & K).

Group Theory-Order of every element of a finite group is a divisor of order of group ( Lecture-13)

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[a^k] = [a^gcd(n,k)] and |a^k| = n/gcd(n,k) Proof (Abstract Algebra)

G is a finite group.If a belongs to G then order of a divides order of G

Centre of a group | Centralizer of an element | Group theory

#12||Order of HK ||Maths for Graduates

H is normal subgroup iff product of two right coset is again a right coset

Quaternion Group (Q8) | Example Group | Group

Lagrange's theorem | lagrange's theorem in hindi | lagrange's theorem proof | group theory