TY - JOUR

T1 - Word and Conjugacy Problems in Groups Gkk+1

AU - Fedoseev, D. A.

AU - Karpov, A. B.

AU - Manturov, V. O.

N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Recently the third named author defined a 2-parametric family of groups Gkn [12]. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups Gkn and dynamical systems led to the discovery of the following fundamental principle: ‘‘If dynamical systems describing the motion of n particles possess a nice codimension one property governed by exactly k particles, then these dynamical systems admit a topological invariant valued in Gkn. The Gkn groups have connections to different algebraic structures, Coxeter groups and Kirillov–Fomin algebras, to name just a few. Study of the Gkn groups led to, in particular, the construction of invariants, valued in free products of cyclic groups. In the present paper we prove that word and conjugacy problems for certain Gkk+1 groups are algorithmically solvable.

AB - Recently the third named author defined a 2-parametric family of groups Gkn [12]. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups Gkn and dynamical systems led to the discovery of the following fundamental principle: ‘‘If dynamical systems describing the motion of n particles possess a nice codimension one property governed by exactly k particles, then these dynamical systems admit a topological invariant valued in Gkn. The Gkn groups have connections to different algebraic structures, Coxeter groups and Kirillov–Fomin algebras, to name just a few. Study of the Gkn groups led to, in particular, the construction of invariants, valued in free products of cyclic groups. In the present paper we prove that word and conjugacy problems for certain Gkk+1 groups are algorithmically solvable.

KW - $G_{n}^{2}$ group

KW - braid

KW - conjugacy problem

KW - dynamical system

KW - group

KW - Howie diagram

KW - invariant

KW - manifold

KW - small cancellation

KW - word problem

KW - G(n)(k) group

UR - http://www.scopus.com/inward/record.url?scp=85084320510&partnerID=8YFLogxK

U2 - 10.1134/S1995080220020067

DO - 10.1134/S1995080220020067

M3 - Article

AN - SCOPUS:85084320510

VL - 41

SP - 176

EP - 193

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 2

ER -