Abstract
A group can be specified as a set of equations. It is shown that there exist canonical term rewriting systems for finite groups which are generated from a finite set of relators such that in this term rewriting system the inversion operator is a defined function. Then it is possible to compute all ground normal forms of these term rewriting systems. Since this set of ground normal forms is generally not generated by a set of free constructors it can be computed using methods developped for ground reducibility tests. We also show that some of the rules defining a group are inductive consequences of other rules in the canonical term rewriting system. This can be proven by inductive completion.
This work is part of the Ph.D. research of the author supervised by Prof. Loos
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Bündgen, R. (1990). Applying term rewriting methods to finite groups. In: Kirchner, H., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1990. Lecture Notes in Computer Science, vol 463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53162-9_49
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DOI: https://doi.org/10.1007/3-540-53162-9_49
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