On a 2-generated infinite 3-group: The presentation problem

  title={On a 2-generated infinite 3-group: The presentation problem},
  author={Said Najati Sidki},
  journal={Journal of Algebra},
  • S. Sidki
  • Published 1 October 1987
  • Mathematics
  • Journal of Algebra
Representations of the Gupta-Sidki group
If p is an odd prime, then the Gupta-Sidki group gp is an infinite 2-generated p-group. It is defined in a recursive manner as a particular subgroup of the automorphism group of a regular tree of
The automorphism tower of groups acting on rooted trees
The group of isometries Aut(T n ) of a rooted n-ary tree, and many of its subgroups with branching structure, have groups of automorphisms induced by conjugation in Aut(T n ). This fact has
A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications
A nilpotent quotient algorithm is described for a certain class of infinite presentations: the so-called finite L-presentations and conjectural descriptions of the lower central series structure of various interesting groups including the Grigorchuk supergroup, the Brunner–Sidki–Vieira group, the Basilica group, and certain generalizations of the Fabrykowski–Gupta group are obtained.
D ec 2 00 6 Groups generated by 3-state automata over a 2-letter alphabet
All finite, abelian, and free groups are classified and detailed information and complete proofs for several groups from the class are provided, with the intention of showing the main methods and techniques used in the classification.
A Note on Invariantly Finitely $L$-Presented Groups
In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly
Nielsen equivalence in Gupta-Sidki groups
For a group G generated by k elements, the Nielsen equivalence classes are defined as orbits of the action of AutF(k), the automorphism group of the free group of rank k, on the set of generating
A just-nonsolvable torsion-free group defined on the binary tree
Abstract A two-generator torsion-free subgroup of the group of finite-state automorphisms of the binary tree is constructed having the properties of being just-nonsolvable and residually
Self-similar groups and their geometry
This is an overview of results concerning applications of self-similar groups generated by automata to fractal geometry and dynamical systems. Few proofs are given, interested reader can find the


Finite automata and Burnside's problem for periodic groups
New examples of infinite periodic finitely-generated groups are constructed. The elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata.
Some infinitep-groups
On the Burnside problem for periodic groups
Narain Gupta 1,. and Said Sidki 2 1 University of Manitoba, Department of Mathematics, Winnipeg, Manitoba R3T 2N2, Canada 2 University of Brasilia, Department of Mathematics, Brasilia, D.F., Brazil
SIDKI, Extensions of groups by free automorphisms
  • Contemp. Math
  • 1984
ALESHIN, Finite automata and the Burnside problem for periodic groups, Mat
  • Zumetki
  • 1972
MERZLYAKOV, On infinite finitely generated periodic groups, Dokl
  • Akud. Nauk
  • 1983
GRIGORCHUK, On the Burnside problem for periodic groups, Funktsional
  • Anal. i Prilozhen
  • 1980
SIDKI, Some infinite p-groups
  • Algebra i Logiku
  • 1983