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Mathematics of Computation

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Divisibility of reduction in groups of rational numbers

Author: Francesco Pappalardi
Journal: Math. Comp. 84 (2015), 385-407
MSC (2010): Primary 11N37; Secondary 11N56
Published electronically: June 27, 2014
MathSciNet review: 3266967
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Abstract: Given a multiplicative group of nonzero rational numbers and a positive integer $ m$, we consider the problem of determining the density of the set of primes $ p$ for which the order of the reduction modulo $ p$ of the group is divisible by $ m$. In the case when the group is finitely generated the density is explicitly computed. Some examples of groups with infinite rank are considered.

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Francesco Pappalardi
Affiliation: Dipartimento di Matematica e Fisica, Università Roma Tre, Largo S. L. Murialdo 1, I–00146, Roma, Italy

Received by editor(s): October 30, 2012
Received by editor(s) in revised form: May 25, 2013
Published electronically: June 27, 2014
Additional Notes: This project was supported in part by G.N.S.A.G.A of I.N.D.A.M.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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