Affiliation:
1. CAUL, Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Abstract
Given tuples a1, …, ak and b in An for some algebraic structure A, the subpower membership problem asks whether b is in the subalgebra of An that is generated by a1, …, ak. For A a finite group, there is a folklore algorithm which decides this problem in time polynomial in n and k. We show that the subpower membership problem for any finite Mal'cev algebra is in NP and give a polynomial time algorithm for any finite Mal'cev algebra with finite signature and prime power size that has a nilpotent reduct. In particular, this yields a polynomial algorithm for finite rings, vector spaces, algebras over fields, Lie rings and for nilpotent loops of prime power order.
Publisher
World Scientific Pub Co Pte Lt
Cited by
12 articles.
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