Divisibility and Laws in Finite Simple Groups
Gady Kozma, Andreas Thom
TL;DR
This paper establishes new bounds on divisibility functions for free groups and constructs short algebraic laws for symmetric and finite simple groups, utilizing classification results.
Contribution
It introduces novel bounds for divisibility functions and constructs short laws for symmetric and finite simple groups based on classification theory.
Findings
New bounds for divisibility functions of free groups
Construction of short laws for symmetric groups
Bounds on law lengths for finite simple groups of Lie type
Abstract
We provide new bounds for the divisibility function of the free group F_2 and construct short laws for the symmetric groups Sym(n). The construction is random and relies on the classification of the finite simple groups. We also give bounds on the length of laws for finite simple groups of Lie type.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Algebra and Geometry