The lower central series of the free partially commutative group

DOI10.1007/BF03025778zbMath0814.20025OpenAlexW2017461533MaRDI QIDQ1204126

Daniel Krob, Gérard H. E. Duchamp

Publication date: 1 March 1993

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/135200

zbMATH Keywords

free grouplower central seriescommutator relationsfree partially commutative groupfree partially commutative Lie algebraMagnus transformation

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Free nonabelian groups (20E05) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Ordered groups (group-theoretic aspects) (20F60) Associated Lie structures for groups (20F40)

Related Items (37)

Algebraic invariants for right-angled Artin groups. ⋮ Universal equivalence of some countably generated partially commutative structures ⋮ ORDERING GRAPH PRODUCTS OF GROUPS ⋮ The strong profinite genus of a finitely presented group can be infinite. ⋮ Normal generation and \(\ell^2\)-Betti numbers of groups. ⋮ Geometry and Combinatorics via Right-Angled Artin Groups ⋮ Coabelian ideals in \(\mathbb{N}\)-graded Lie algebras and applications to right angled Artin Lie algebras ⋮ Mal’tsev bases for partially commutative nilpotent groups ⋮ Conjugacy \(p\)-separability of right-angled Artin groups and applications. ⋮ Small \(C^1\) actions of semidirect products on compact manifolds ⋮ Special cube complexes revisited: a quasi-median generalization ⋮ Universal equivalence of partially commutative Lie algebras ⋮ Right‐angled Artin pro‐p$p$ groups ⋮ Centralizers in partially commutative Lie algebras ⋮ Homology growth, hyperbolization, and fibering ⋮ The strong Atiyah conjecture for right-angled Artin and Coxeter groups. ⋮ Elementary equivalence of partially commutative Lie rings and algebras ⋮ Universal equivalence of partially commutative metabelian Lie algebras ⋮ RAAGs in diffeos ⋮ Divergence and quasimorphisms of right-angled Artin groups. ⋮ On the partially commutative shuffle product ⋮ On the decidability of the equivalence problem for partially commutative rational power series ⋮ Multiplicities: A deterministic view of nondeterminism ⋮ Toric complexes and Artin kernels ⋮ ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS ⋮ Bases for partially commutative Lie algebras ⋮ Residual properties of graph manifold groups ⋮ Right angled Artin groups and partial commutation, old and new ⋮ Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables ⋮ The associated Lie algebra of a right-angled Coxeter group ⋮ Residually free 3-manifolds ⋮ Direct products, overlapping actions, and critical regularity ⋮ Groups with the same cohomology as their pro-\(p\) completions. ⋮ On universal equivalence of partially commutative Lie algebras defined by graphs without triangles and squares and with no isolated vertices ⋮ On Universal Equivalence of Partially Commutative Metabelian Lie Algebras ⋮ Graded components of the Lie algebra associated with the lower central series of a right-angled Coxeter group ⋮ Diagram groups are totally orderable.

Cites Work

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• Lyndon bases of free partially commutative Lie algebras
• On the decidability of the equivalence problem for partially commutative rational power series
• The free partially commutative Lie algebra: Bases and ranks
• Free partially commutative structures
• Combinatorial problems of commutation and rearrangements
• Isomorphisms of Graph Groups
• Groups with the same lower Central Sequence as a Relatively Free Group. I The Groups
• On Ordered Division Rings

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