We present methods to construct representations of finitely presented groups. In wellconditioned examples it is possible to use GrΓΆbner 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
Constructing Representations of Finite Groups and Applications to Finitely Presented Groups
β Scribed by W Plesken; B Souvignier
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 180 KB
- Volume
- 202
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
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.
We formulate an algorithm for calculating a representation by unipotent matrices over the integers of a finitely-generated torsion-free nilpotent group given by a polycyclic presentation. The algorithm works along a polycyclic series of the group, each step extending a representation of an element o
We describe an algorithmic test, using the "standard polynomial identity" (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When n-dimensional irreducible representations do exi
A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representa-Ε½ . tion developed by Magnus 1939, Ann. of Math. 40, 764α768 for metabelian Ε½ groups. Using this condition and a construction due to Baumsla