Notes on extended equation solvability and identity checking for groups
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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 phrasesequation solvability identity checking solvable group
Mathematics Subject Classification20F10 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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