Divisibility and Laws in Finite Simple Groups

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.

20 pages, no figures; v3 completely rewritten with new co-author and new results

References in corpus (3)

• Growth in finite simple groups of Lie type
• On the maximum orders of elements of finite almost simple groups and primitive permutation groups
• Finite primitive permutation groups and regular cycles of their elements

Cited by in corpus (2)

• The topology of local commensurability graphs
• Local commensurability graphs of solvable groups