On the q-tensor square of a group

We study the non-abelian tensor square modulo q of a group, where q is a non-negative integer, via an operator v(q) in the class of groups. Structural properties and finiteness conditions of v(q)(G) are investigated. We compute the non-abelian tensor square modulo q of cyclic groups and develop a theory for computing v(q)(G) and some of its relevant sections for polycyclic groups G. This extends the existing theory from the case q = 0 to all non-negative integers q. Additionally, a table of examples is produced with the help of the GAP system.