The equation solvability problem over supernilpotent algebras with Mal’cev term
2018 ◽
Vol 28
(06)
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pp. 1005-1015
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Keyword(s):
In 2011, Horváth gave a new proof that the equation solvability problem over finite nilpotent groups and rings is in P. In the same paper, he asked whether his proof can be lifted to nilpotent algebras in general. We show that this is in fact possible for supernilpotent algebras with a Mal’cev term. However, we also describe a class of nilpotent, but not supernilpotent algebras with Mal’cev term that have co-NP-complete identity checking problems and NP-complete equation solvability problems. This proves that the answer to Horváth’s question is negative in general (assuming P[Formula: see text]NP).
2011 ◽
Vol Vol. 13 no. 4
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2017 ◽
Vol 27
(02)
◽
pp. 259-272
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2019 ◽
Vol 30
(03)
◽
pp. 607-623
1985 ◽
Vol 25
(3)
◽
pp. 601-618
◽
2008 ◽
Vol 47
(1)
◽
pp. 250-258
◽
2014 ◽
Vol 51
(4)
◽
pp. 547-555
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2018 ◽
Vol 10
(1)
◽
pp. 67-78
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1985 ◽
Vol 21
(5)
◽
pp. 969-999
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