  The purpose of this article is to extend the earliest results of A.A. Brudno,
connecting topological entropy of a subshift X over $\mathbb{N}$ to the
Kolmogorov complexity of words in X, to subshifts over computable groups that
posses computable F{\o}lner monotilings, which we introduce in this work. The
classical examples of such groups are the groups $\mathbb{Z}^d$ and the groups
of upper-triangular matrices with integer entries. Following the work of B.
Weiss we show that the class of such groups is closed under group extensions.
