Cancellation diagrams with non-positive curvature (Q2702052)

One of the most typical problems of the combinatorial group theory is the solution of the conjugacy problem for groups the presentations of which satisfy various small cancellation conditions. The current paper suggests the small cancellation conditions \(W^*\) and \(W\) which are dual to each other. These conditions reflect the non-positive curvature of the group presentations. The condition \(W^*\) is a generalization of the well known conditions \(C(6)\), \(C(4)\&T(4)\), \(C(3)\), \(T(6)\). The condition \(W\) is a generalization of the same conditions and also of the condition \(W(6)\) of Juhász. The central result of the paper is the solution of the conjugacy problem for groups satisfying the condition \(W^*\) or the condition \(W\).NEWLINENEWLINEFor the entire collection see [Zbl 0940.00028].