0000000000855244

AUTHOR

Eddy Godelle

showing 2 related works from this author

PreGarside monoids and groups, parabolicity, amalgamation, and FC property

2012

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside g…

Property (philosophy)[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Group (mathematics)General Mathematics010102 general mathematics20F36Group Theory (math.GR)Type (model theory)01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics::Group TheoryProduct (mathematics)0103 physical sciencesFOS: Mathematics010307 mathematical physicsWord problem (mathematics)0101 mathematicsAlgebraic numberMathematics - Group TheoryMathematics
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The conjugacy problem in subgroups of right-angled Artin groups

2009

We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.

CombinatoricsMathematics::Group TheoryConjugacy problemBraid groupGeometry and TopologyNatural classGraphMathematicsJournal of Topology
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