Bounding the free spectrum of nilpotent algebras of prime power order
- 13 Downloads
Let A be a finite nilpotent algebra in a congruence modular variety with finitely many fundamental operations. If A is of prime power order, then it is known that there is a polynomial p such that for every n ∈ ℕ, every n-generated algebra in the variety generated by A has at most 2p(n) elements. We present a bound on the degree of this polynomial.
Unable to display preview. Download preview PDF.
- [BS81]S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics, Vol. 78, Springer, New York–Berlin, 1981.Google Scholar
- [FM87]R. Freese and R. N. McKenzie, Commutator Theory for Congruence Modular Varieties, London Mathematical Society Lecture Note Series, Vol. 125, Cambridge University Press, Cambridge, 1987.Google Scholar
- [Gum83]H. P. Gumm, Geometrical methods in congruence modular algebras, Memoirs of the American Mathematical Society 286 (1983).Google Scholar
- [Hig67]G. Higman, The orders of relatively free groups, in Proceedings of the International Conference on the Theory of Groups (Canberra, 1965), Gordon and Breach, New York, 1967, pp. 153–165.Google Scholar
- [HM88]D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics, Vol. 76, American Mathematical Society, Providence, RI, 1988.Google Scholar
- [Kre18]S. Kreinecker, Closed function sets on groups of prime order, https://arxiv.org/abs/1810.09175.Google Scholar
- [MMT87]R. N. McKenzie, G. F. McNulty and W. F. Taylor, Algebras, Lattices, Varieties. Volume I, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, California, 1987.Google Scholar
- [Smi76]J. D. H. Smith, Mal’cev Varieties, Lecture Notes in Mathematics, Vol. 554, Springer, Berlin, 1976.Google Scholar
- [Wir19]A. Wires, On Supernilpotent Algebras, Algebra Universalis 80 (2019), Art. 1.Google Scholar