Computing in groups with exponent six (Q2702048)

Let \(B(d,n)\) be the free group on \(d\) generators with exponent \(n\). Let \(C(r,s)\) denote the largest two-generator group with exponent six generated by elements of orders \(r\) and \(s\). The nature of sixth power relations required to provide finiteness for the group \(B(2,6)\) is investigated. It is shown that \(B(2,6)\) has a presentation on 2 generators with 81 relations which is derived from a polycyclic presentation. It is given a program to construct a polycyclic presentation for \(B(2,6)\) which shows the structure of the group. To understand \(B(2,6)\) better presentations for the groups \(C(2,2)\), \(C(2,3)\), \(C(3,3)\), \(C(2,6)\) and \(C(3,6)\) are obtained.NEWLINENEWLINEFor the entire collection see [Zbl 0940.00028].