Countable sequenceable groups

AbstractA finite group G having n elements is said to be sequenceable if there exists an arrangement b1, b2…,bn of its elements such that b1, b1b2,…, b1b2⋯ b1 is also an arrangement of the elements of G. This definition can be extended to the case when G is countably infinite by requiring the existence of a sequence b1, b2,…, containing each element of G exactly once, such that the sequence b1,b1b2,… also contains each element of G exactly once. With this definition every countably-infinite group is sequenceable