- journal articles metadata
European Mathematical Society Publishing House
2024-03-19 09:53:22
2
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JCA&vol=1&iss=3&update_since=2024-03-19
Journal of Combinatorial Algebra
J. Comb. Algebra
JCA
2415-6302
2415-6310
Combinatorics
Group theory and generalizations
10.4171/JCA
http://www.ems-ph.org/doi/10.4171/JCA
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2017
3
Multifraction reduction II: Conjectures for Artin–Tits groups
Patrick
Dehornoy
Université de Caen and and Institut Universitaire de France, France
Artin–Tits monoid, Artin–Tits group, gcd-monoid, enveloping group, word problem, multifraction, reduction, semi-convergence, cross-confluence, tame reduction, van Kampen diagram, embeddability
Multifraction reduction is a new approach to the word problem for Artin–Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite system (“reduction”) that extends free group reduction. In this paper, we show that assuming that reduction satisfies a weak form of convergence called semi-convergence is sufficient for solving the word problem for the enveloping group, and we connect semi-convergence with other conditions involving reduction. We conjecture that these properties are valid for all Artin–Tits monoids, and provide partial results and numerical evidence supporting such conjectures.
Group theory and generalizations
Category theory; homological algebra
Computer science
229
287
10.4171/JCA/1-3-1
http://www.ems-ph.org/doi/10.4171/JCA/1-3-1
Lie algebras and torsion groups with identity
Efim
Zelmanov
University of California – San Diego, La Jolla, USA
The Burnside problem, pro-$p$ groups, PI-algebras, Lie algebras
We prove that a finitely generated Lie algebra $L$ such that (i) every commutator in generators is ad-nilpotent, and (ii) $L$ satisfies a polynomial identity, is nilpotent. As a corollary we get that a finitely generated residually-$p$ torsion group whose pro-$p$ completion satisfies a pro-$p$ identity is finite.
Group theory and generalizations
Associative rings and algebras
289
340
10.4171/JCA/1-3-2
http://www.ems-ph.org/doi/10.4171/JCA/1-3-2