#157: Group with a unique subgroup of finite order is normal: proof

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#158: Group with a unique subgroup of finite order is normal: Example #158: Group with a unique subgroup of finite order is normal: Example
If H is the only subgroup of order o(H) in the finite group G, then H is normal in G . If H is the only subgroup of order o(H) in the finite group G, then H is normal in G .
G has unique subgroup then it is normal G has unique subgroup then it is normal
Sylow Sylow's Theorem applied to a group of order 40
Subgroups of Finitely Generated Groups (Algebra 1: Lecture 11 Video 4) Subgroups of Finitely Generated Groups (Algebra 1: Lecture 11 Video 4)
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
Sylow Sylow's third theorem/ sylow p-subgroup of a finite group G is unique iff its normal/m.sc maths
6.14-6.15- b=a^s generates cyclic subgroup H of G containing n/d elements, d is the gcd of n and s. 6.14-6.15- b=a^s generates cyclic subgroup H of G containing n/d elements, d is the gcd of n and s.