We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9, author = {Thierry de la Rue}, title = {An extension which is relatively twofold mixing but not threefold mixing}, journal = {Colloquium Mathematicae}, volume = {100}, year = {2004}, pages = {271-277}, zbl = {1067.37006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9} }
Thierry de la Rue. An extension which is relatively twofold mixing but not threefold mixing. Colloquium Mathematicae, Tome 100 (2004) pp. 271-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-9/