A short proof, using graphs and groupoids, is given of Brodskĭı’s theorem that torsion-free one-relator groups are locally indicable.

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

We give experimental support for a conjecture of Louder and Wilton saying that words imprimitivity rank greater than two yield hyperbolic one-relator groups.

We show that a class of cyclically pinched one-relator groups admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on 2 generators.

We prove that Whitehead’s algorithm for solving the automorphism problem in a fixed free group Fk has strongly linear time generic-case complexity. This is done by showing that the “hard” part of the algorithm terminates in linear time on an exponentially generic set of input pairs. We then apply these results to one-relator groups. We obtain a Mostow-type isomorphism rigidity result for random...

The United States Court of Appeals for the Second Circuit recently issued a decision that could narrow the scope of the prosecution of cases brought against health care providers under the False Claims Act, 31 U.S.C. § 3729, et seq. (the “Act”). This decision, United States ex rel. Mikes v. Straus, (http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=2nd&navby=case&no=006269) does significan...

Magnus’ Freiheitssatz [20] states that if a group is defined by presentation with m generators and single cyclically reduced relator, this relator contains the last generating letter, then first $$m-1$$ letters freely generate free subgroup. We study an analogue of theorem in Gromov density model random groups [14], showing phase transition phenomenon at $$d_r = \min \{\frac{1}{2}, 1-\log _{2m-...

This paper presents a supervised method for the detection and extraction of Causal Relations from open domain text. First we give a brief outline of the definition of causation and how it relates to other Semantic Relations, as well as a characterization of their encoding. In this work, we only consider marked and explicit causations. Our approach first identifies the syntactic patterns that ma...