We present methods to construct representations of finitely presented groups. In wellconditioned examples it is possible to use Gröbner base and resultant methods to solve the system of algebraic equations obtained by evaluating the relations on matrices with indeterminates as entries. For more comp
✦ LIBER ✦
Constructing Finitely Presented Simple Groups That Contain Grigorchuk Groups
✍ Scribed by Claas E. Röver
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 188 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We construct infinite finitely presented simple groups that have subgroups isomorphic to Grigorchuk groups. We also prove that up to one possible exception all previously known finitely presented simple groups are torsion locally finite.
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## dedicated to helmut wielandt on the occasion of his 90th birthday Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t ∼ = H. In this