Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 246–256 | Cite as

Notes on extended equation solvability and identity checking for groups

  • M. KompatscherEmail author


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.

Key words and phrases

equation solvability identity checking solvable group 

Mathematics Subject Classification

20F10 20F12 20D10 08A70 


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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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of AlgebraMFF UKPraha 8Czech Republic

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