Finitely generated groups (mod 𝑝)

Murty, M. Ram

doi:10.1090/S0002-9939-1994-1195485-7

Finitely generated groups (mod $p$)
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Proc. Amer. Math. Soc. 122 (1994), 37-45 Request permission

Abstract:

Given r mutually coprime natural numbers ${a_1}, \ldots ,{a_r}$ greater than 1 and an irreducible polynomial $f(t)$ with integer coefficients, we investigate how the structure of the group generated by ${a_1}, \ldots ,{a_r} \bmod p$ varies as the prime p varies subject to the condition that $f(t)$ splits completely $\bmod \;p$.

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The integer solutions of the equation

1