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arXiv · 1805.01796

Bounding the free spectrum of nilpotent algebras of prime power order

Erhard Aichinger
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Abstract

Let $\mathbf{A}$ be a finite nilpotent algebra in a congruence modular variety with finitely many fundamental operations. If $\mathbf{A}$ is of prime power order, then it is known that there is a polynomial $p$ such that for every $n \in \mathbb{N}$, every $n$-generated algebra in the variety generated by $\mathbf{A}$ has at most $2^{p(n)}$ elements. We present a bound on the degree of this polynomial.

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Erhard Aichinger. 2019-01-23. Bounding the free spectrum of nilpotent algebras of prime power order. https://doi.org/10.1007/s11856-019-1846-x

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