On the shortest identity in finite simple groups of Lie type

DOI10.1515/JGT.2010.039zbMath1234.20019arXiv0808.0622MaRDI QIDQ3083480

Uzy Hadad

Publication date: 22 March 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.0622

zbMATH Keywords

identitiesfinite simple groupsfinite groups of Lie typelaws

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06) Quasivarieties and varieties of groups (20E10)

Related Items (9)

Divisibility and laws in finite simple groups. ⋮ Intersection growth in groups ⋮ Short laws for finite groups and residual finiteness growth ⋮ IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS ⋮ Bertrand's postulate and subgroup growth. ⋮ Bounding the residual finiteness of free groups ⋮ Babai's conjecture for high-rank classical groups with random generators ⋮ No iterated identities satisfied by all finite groups ⋮ About the length of laws for finite groups

Cites Work

• On finitely generated profinite groups. I: Strong completeness and uniform bounds. II: Products in quasisimple groups.
• Word maps, conjugacy classes, and a noncommutative Waring-type theorem.
• Residual properties of free groups. III
• Word maps have large image.
• Some remarks concerning the Ree groups of type \((G_2)\)
• Identical relations in finite groups
• On the girth of random Cayley graphs
• Word maps and Waring type problems
• A product decomposition for the classical quasisimple groups
• Residual properties of free groups, II
• A basis for the laws of a class of simple groups
• Varieties and simple groups
• A basis for the laws of 𝑃𝑆𝐿(2,5)
• Residually finite groups
• On the laws of certain linear groups
• Two-variable laws for a class of finite simple groups
• Residual properties of free groups

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