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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 theKolmogorov complexity of words in X, to subshifts over computable groups thatposses computable F{\o}lner monotilings, which we introduce in this work. Theclassical examples of such groups are the groups $\mathbb{Z}^d$ and the groupsof 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.

Computable F{\o}lner monotilings and a theorem of Brudno I