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RESEARCH PRODUCT
A presentation and a representation of the Held group
Jörg Hrabě De Angelissubject
AlgebraPure mathematicsPresentation of a groupHeld groupG-moduleKlein four-groupSymmetric groupGeneral MathematicsQuaternion groupSchur multiplierMathematicsMathieu group M24description
In this note we give a brief description of a new presentation of the Held group, which is deduced only from the original work of D. Held in 1969, who shows that a finite simple group, having the same centralizer of a 2-central involution as in the Mathieu group M24, is M24, L5(2) or a group of order 4.030.387.200. The first complete uniqueness proof for the latter case was given by L. Soicher in 1991. The generators and relations occurring here are easy to verify by a simple Todd–Coxeter algorithm. It is an easy task to get a new uniqueness and existence proof of the Held group from this result. Also basic facts like the Schur Multiplier or the automorphism group of the Held group follow from this representation. The simplicity of the relations can be seen by a notation similar to the Coxeter graph. The presentation only consists of defining relations of three local subgroups of the Held group. An explicit 51-dimensional irreducible GF(2)-representation of the Held group is given.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1996-04-01 | Archiv der Mathematik |