Let $C$ be an abelian additive group and write e for a generator of $C$. The elements of $C$ are then $0,e,2e,3e,\dots,(n-1)e$. If $C$ is finite, prove that the element $ke$ is another generator of $C$ if and only if $k$ and $n$ are relatively prime.
Generators of a finite additive cyclic group
2
$\begingroup$
abstract-algebra
finite-groups
cyclic-groups
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1Can you argue the 'if' and/or the 'only if' part? – 2012-11-12
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0I do not believe so. – 2012-11-12