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## Revista de Ciencias

*Print version* ISSN 0121-1935

#### Abstract

GARZON R., Álvaro. **𝑝**-cycles, *S*_{2} -sets and Curves with Many Points.* rev. cienc.* [online]. 2017, vol.21, n.1, pp.55-78.
ISSN 0121-1935.

We construct S 2-sets contained in the integer interval I q-1 = [1,q - 1] with q = 𝑝 n , 𝑝 a prime number and n ∈ Z+, by using the 𝑝-adic expansion of integers. Such sets come from considering 𝑝-cycles of length n. We give some criteria in particular cases which allow us to glue them to obtain good S 2-sets. After that we construct algebraic curves over the finite field 𝔽 q with many rational points via minimal (𝔽𝑝, 𝔽𝑝)-polynomials whose exponent set is an S 2-set.

**Keywords
:
**𝑝-adic expansion; *S* _{2}-sets; finite field; Kummer cover; rational points.

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