A result on the orders of the reductions of an element of the group of S-units of a number field is obtained by investigating three height functions for groups of S-units of number fields which are analogous to local, global and canonical height functions for elliptic curves.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-4,
author = {Stefan Bara\'nczuk},
title = {Height Functions for Groups of S-units of Number Fields and Reductions Modulo Prime Ideals},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {63},
year = {2015},
pages = {25-31},
zbl = {06488954},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-4}
}
Stefan Barańczuk. Height Functions for Groups of S-units of Number Fields and Reductions Modulo Prime Ideals. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 25-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-4/