Non-product property of the digital fundamental group

For given two digital images both equipped with each digital connectedness, we show that the digital fundamental groups of both images do not necessarily lead to the digital fundamental group of the product image. In order to prove the non-product property of the digital fundamental group of the digital product image, we need the notion of product image and some calculation of the digital 8-fundamental group of the digital 8-pseudotorus in Z4 by means of a counterexample.