Digital topological groups

In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate types, based on the details of the continuity required of the group multiplication. We define NP₁- and NP₂-digital topological groups, and investigate their properties and algebraic structure. The NP₂-type is very restrictive, and we give a complete classification of NP₂-digital topological groups. We also give many examples of NP₁-digital topological groups. We define digital topological group homomorphisms, and describe the digital counterpart of the first isomorphism theorem.