Deciding finiteness of matrix groups in positive characteristic. (English) Zbl 1189.20043
Summary: We present a new algorithm to decide finiteness of matrix groups defined over a field of positive characteristic. Together with previous work for groups in zero characteristic, this provides the first complete solution of the finiteness problem for finitely generated matrix groups over a field. We also give an algorithm to compute the order of a finite matrix group over a function field of positive characteristic by constructing an isomorphic copy of the group over a finite field. Our implementations of these algorithms are publicly available in Magma.
MSC:
| 20H20 | Other matrix groups over fields |
| 68W30 | Symbolic computation and algebraic computation |
| 20-04 | Software, source code, etc. for problems pertaining to group theory |
Keywords:
finiteness problem; order problem; algorithms; matrix groups over function fields; finitely generated matrix groups; general linear groups; exponential-time algorithmsReferences:
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