On 3-generated 6-transposition groups (Q6644319)

Let \(G\) be a group, if \(G\) is generated by a normal set of involutions \(D\) such that the order of the product of any two elements from \(D\) does not exceed an integer \(n\), then \(G\) is said to be an \(n\)-transposition group.\N\NThe purpose of the paper under review is to classify \(6\)-transposition groups \(G =\langle x, y, z\rangle\) with \(x,y,z \in D\) such that \([x,y]=1\), and one of the other two products, say \(xz\), is not of order \(6\). The results are described in detail in the main Theorem (the statement of which is too complex to be reported here). The reviewer points out that, in particular, all such groups turn out to be finite and isomorphic to quotients of finite groups whose presentations are given in the final appendix. In the proofs, it is essential to make use of the software \textsf{GAP}.