Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple Groups

Abstract

The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.

version 4; 40 pages, 1 figure; an error in the statement of Theorem 1 is corrected (the set $S$ should not be allowed to contain proper powers); v3: a flaw in the proof of the main theorem is corrected (the assumtions of maps' being non-exceptional are removed from the hypotheses of Estimating Lemma 1 and Inductive Lemma 2)

Cited by in corpus (6)

• Finitely generated infinite simple groups of infinite commutator width
• Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length
• Ranks of subgroups in boundedly generated groups
• On torsion-free groups with finite regular file bases
• Groups with finitely many conjugacy classes and their automorphisms
• Finitely generated groups with polynomial index growth