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

(Corollary:3) Every group of prime order is cyclic.

order of element is a divisor of order of group

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

Every group of prime order is cyclic (group theory ) |NERDY CREW

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

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Every subgroup of a cyclic group is cyclic.