IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS

DOI10.1017/S0017089513000396zbMath1318.20014arXiv1211.6575OpenAlexW2962873838MaRDI QIDQ5415966

Alexander Lubotzky

Publication date: 19 May 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.6575

zbMATH Keywords

finite simple groupsword maps

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Finite simple groups and their classification (20D05) Algebraic geometry over groups; equations over groups (20F70)

Related Items (14)

On sequences of word maps of compact topological groups ⋮ Computing \(n\)-th roots in \(\text{SL}_{2}\) and Fibonacci polynomials ⋮ Word maps with constants on symmetric groups ⋮ Criteria for equidistribution of solutions of word equations on \(\mathrm{SL}(2)\). ⋮ Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. ⋮ Unnamed Item ⋮ Word problems for finite nilpotent groups ⋮ Words have bounded width in ⋮ On the combinatorics of commutators of Lie algebras ⋮ On the symmetry of images of word maps in groups ⋮ Word maps in finite simple groups ⋮ Word images in symmetric and classical groups of Lie type are dense ⋮ Geometry of word equations in simple algebraic groups over special fields ⋮ On rational and concise words.

Cites Work

• On the image of a noncommutative polynomial.
• The Waring problem for finite simple groups.
• The Ore conjecture.
• Probabilistic generation of finite simple groups
• The probability of generating a finite classical group
• On the shortest identity in finite simple groups of Lie type

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