Research output: Contribution to journal › Article › peer-review
Word and Conjugacy Problems in Groups Gkk+1. / Fedoseev, D. A.; Karpov, A. B.; Manturov, V. O.
In: Lobachevskii Journal of Mathematics, Vol. 41, No. 2, 01.02.2020, p. 176-193.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 24957220