Theorem : If G be a cyclic group of order n then for every divisor m of n there exists a subgroup.

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30. Theorem: For each positive divisor 30. Theorem: For each positive divisor 'd' of 'n', there is a unique subgroup of G of order d(proof)
G be a cyclic group of order n.Then for every+ve divisor m of n,G has a unique subgroup H of order m G be a cyclic group of order n.Then for every+ve divisor m of n,G has a unique subgroup H of order m
G is cyclic group of order n, then for any divisor d of n there is unique subgroup of order d #bsc G is cyclic group of order n, then for any divisor d of n there is unique subgroup of order d #bsc
Let G be cyclic group of order n then a_k is generator of G if gcd(k, n)=1 Let G be cyclic group of order n then a_k is generator of G if gcd(k, n)=1
Group Theory | Cyclic Group | Properties Of Cyclic Group | Discrete Mathematics Group Theory | Cyclic Group | Properties Of Cyclic Group | Discrete Mathematics
A Cyclic Group of Order n Has Exactly One Subgroup of Order d (When d Divides n) | Theorem | CSS A Cyclic Group of Order n Has Exactly One Subgroup of Order d (When d Divides n) | Theorem | CSS
Lecture#58:Let G be a cyclic Group of Order n,there is a unique Subgroup of G for a +ve divisor of n Lecture#58:Let G be a cyclic Group of Order n,there is a unique Subgroup of G for a +ve divisor of n
if G be finite group and a be any element of G s.t. o(a)=n them a^m=e iff n|m if G be finite group and a be any element of G s.t. o(a)=n them a^m=e iff n|m