In this article a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. The usual results on small cancellation groups are then shown to hold in this new setting with only slight modifications. For example, arbitrary dimensional versions of the Poincaré construction and the Cayley complex are described.

In the present paper we develop a small cancellation theory for associative algebras with basis of invertible elements. Namely, study quotients group algebra free and introduce three axioms corresponding defining relations. We show that obtained ring is non-trivial. Moreover, this enjoys global filtration agrees relations, find as vector space establish structure theorems. also provide revision...

in this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎in particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.

background and objectives: surgical cancelation is a significant source of time and resource waste, patientsafety risk, and stress for patients and their families. in this study, a risk management-based approach is developed to prioritize factors contributing to surgical cancellation. methods: factors leading to surgical cancellation were comprehensively classified based on literature review.a...

In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the fi...

In these notes we detail the geometrical approach of small cancellation theory used by T. Delzant and M. Gromov to provide a new proof of the infiniteness of free Burnside groups and periodic quotients of torsion-free hyperbolic groups.

Background and Objectives: Surgical cancelation is a significant source of time and resource waste, patient safety risk, and stress for patients and their families. In this study, a risk management-based approach is developed to prioritize factors contributing to surgical cancellation. Methods: Factors leading to surgical cancellation were comprehensively classified based on literature review...