## Abstract

Recently the third named author defined a 2-parametric family of groups G^{k}_{n} [12]. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups G^{k}_{n} 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 G^{k}_{n}. The G^{k}_{n} groups have connections to different algebraic structures, Coxeter groups and Kirillov–Fomin algebras, to name just a few. Study of the G^{k}_{n} 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 G^{k}_{k+1} groups are algorithmically solvable.

Original language | English |
---|---|

Pages (from-to) | 176-193 |

Number of pages | 18 |

Journal | Lobachevskii Journal of Mathematics |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2020 |

## Keywords

- $G_{n}^{2}$ group
- braid
- conjugacy problem
- dynamical system
- group
- Howie diagram
- invariant
- manifold
- small cancellation
- word problem
- G(n)(k) group