Conjugation-free groups, lower central series and line arrangements
type: Dataset
description: The quotients $G_k/G_{k+1}$ of the lower central series of a finitely presented group $G$ are an important invariant of this group. In this work we investigate the ranks of these quotients in the case of a certain class of conjugation-free groups, which are groups generated by $x_1,...,x_n$, and having only cyclic relations: $$ x_{i_t} x_{i_{t-1}} ... x_{i_1} = x_{i_{t-1}} ... x_{i_1} x_{i_t} = ... = x_{i_1} x_{i_t} ... x_{i_2}.$$ Using tools from group theory and from the theory of line arrangements we explicitly find these ranks, which depend only at the number and length of these cyclic relations. It follows that for these groups the associated graded Lie algebra $gr(G)$ decomposes, in any degree, as a direct product of local components.
landing page: https://hal.science/hal-00826941
keyword: 52c35-20f14-20f40-14h30
keyword: associated-graded-lie-algebra
keyword: conjugation-free-groups
keyword: infoeu-reposemanticspreprint
keyword: line-arrangements
keyword: lower-central-series
keyword: mathmath-grmathematics-mathgroup-theory-mathgr
keyword: preprints-working-papers-
issued: 2026-05-10T23:51:32.031573
modified: 2026-05-10T23:51:32.031577
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Conjugation-free groups, lower central series and line arrangements
type: Distribution
format: HTML
access URL: https://hal.science/hal-00826941
issued: 2026-05-10T23:51:32.046689
modified: 2026-05-10T23:51:32.017014