6533b837fe1ef96bd12a2727
RESEARCH PRODUCT
PreGarside monoids and groups, parabolicity, amalgamation, and FC property
Eddy GodelleLuis Parissubject
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 TheoryMathematicsdescription
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 groups and that is closed by amalgamation along parabolic subgroups. Finally, we make an algebraic and combinatorial study on FC type preGarside groups and their parabolic subgroups.
year | journal | country | edition | language |
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2012-04-25 |