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 Horváth and Szabó; the term constructed in their proof depends on the underlying group. In this paper we provide a uniform term extension that induces hard problems. 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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Acknowledgement
The author would like to thank Attila Földvári and Gábor Horváth for their valuable feedback on earlier versions of this paper.
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This work has been supported by Charles University Research Centre programs No. PRIMUS/SCI/12 and No. UNCE/SCI/022, as well as grant 18-20123S of the Czech Grant Agency (GAČR).
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Kompatscher, M. Notes on extended equation solvability and identity checking for groups. Acta Math. Hungar. 159, 246–256 (2019). https://doi.org/10.1007/s10474-019-00924-7
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DOI: https://doi.org/10.1007/s10474-019-00924-7