  Let $G$ be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on
$G$ via the multiresolution analysis method. In this article, a
characterization of wavelet sets on $G$ is established, which provides another
method for the construction of wavelets. As an application, the relation
between multiresolution analyses and wavelets determined from wavelet sets is
also presented. To some extent, these results positively answer a question
mentioned by P. Mahapatra and D. Singh in [Bull. Sci. Math. 167 (2021), Paper
No. 102945, 20 pp].
