Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups

Groups of Fibonacci Type Revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway’s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repovš, they have ...

On the Structure of Some Deficiency Zero Groups

On the second order first zagreb index

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

Cyclically presented groups in which the relators involve at most three generators

Cyclically presented groups Gn(w) in which w involves at most three generators are studied. We classify when such groups have infinite abelianizations and apply this result to the groups Gn(x1x1+kx 1+`). As a further corollary we give sufficient conditions for the natural HNN extension of Gn(w) to be a high-dimensional knot group. By continuing Cavicchioli, Repovš, and Spaggiari’s investigation...

Addendum to “random Walk on Random Groups” by M. Gromov

Written at the request of GAFA’s Editorial Board, with the goal of explicating some aspects of M. Gromov’s paper [2]. Section 1 recalls the construction of the random group, while section 2 contains a proof that the random group has property (T) based on the ideas from the preprint. The appendix defines CAT(0) spaces and works out in detail some geometric propositions from the preprint used in ...