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arXiv · 1808.07776

Some notes on extended equation solvability and identity checking for groups

Michael Kompatscher
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Abstract

Every finite non-nilpotent group can be extended by a term operation such that solving equations in the resulting algebra is NP-complete and checking identities is co-NP-complete. This result was firstly proven by Horv\'ath and Szab\'o; the term constructed in their proof depends on the underlying group. In this paper we provide a uniform term extension that induces hardness. In doing so we also characterize a big class of solvable, non-nilpotent groups for which extending by the commutator operation suffices.

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Michael Kompatscher. 2018-08-23. Some notes on extended equation solvability and identity checking for groups. https://arxiv.org/abs/1808.07776

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