Algorithms for the Tits alternative and related problems

作者：Detinko A S^*; Flannery D L; O'Brien E A

来源：Journal of Algebra, 2011, 344(1): 397-406.

DOI：10.1016/j.jalgebra.2011.06.036

• Finitely generated linear group
• Solvable-by-finite group
• Decision problems
• Algorithm

We present an algorithm to decide whether a finitely generated linear group over an infinite field is solvable-by-finite, thereby obtaining a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is nilpotent-by-finite, abelian-by-finite, or central-by-finite. Implementations of the algorithms are publicly available in MAGMA.

• 出版日期2011-10-15