let G be a finite abelian group k a fixed positive integer a

let G be a finite abelian group k a fixed positive integer and H={a^k|a in G }. prove that h is a subgroup of G

Given that G is a finite abelian group

and k a fixed positive integer

For k =0 we have aⁿ=a⁰ = e belongs to G

Hence identity element belongs to G

K, being a positive integer can be written as r modn where 0<r<n

For r, we have n-r such that

a^r * a^(n-r) =e

Hence all elements have inverse.

So H is a subgroup.

$let G be a finite abelian group k a fixed positive integer and H={a^k|a in G }. prove that h is a subgroup of G let G be a finite abelian group k a fixed posit$

let G be a finite abelian group k a fixed positive integer a

Solution

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