Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 246–256

# Notes on extended equation solvability and identity checking for groups

Article

## 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.

## Key words and phrases

equation solvability identity checking solvable group

## Mathematics Subject Classification

20F10 20F12 20D10 08A70

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