Knowing the factorisation of $g\in Z_p$, how to calculate the size of $\{g^i:0\leq i \leq p\}$? By $Z_p$ I mean the integers modulo $p$, where $p$ is prime.
Generated subgroup size
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abstract-algebra
finite-groups
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5The ordinary prime factorization of $g$ does not tell us much about the order of $g$ modulo $p$. – 2012-03-21
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1I believe it is still unknown whether $2$ is a primitive root modulo infinitely many primes; of course, $2$ has a very simple factorization... – 2012-03-22