Research

My current interests are structure theory, equations and computational problems for general algebras. Here an algebra is set with some operations that describe the computations that can be conducted with its elements, e.g. a group, a lattice...

Some of my recent results:

Editorial board

Algebra Universalis

Publications

In reverse chronological order:
  1. P. Mayr and P. Wynne. Clonoids between modules. Submitted 2023. [pdf]
  2. P. Mayr. Vaughan--Lee's nilpotent loop of size 12 is finitely based. Algebra Universalis 85 (2024), no. 1, Paper No. 2, 12 pp. [pdf]
  3. P. Mayr. On the complexity dichotomy for the satisfiability of systems of term equations over finite algebras. 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), Leibniz International Proceedings in Informatics (LIPIcs) 272, 66:1–66:12, 2023. [pdf]
  4. P. Mayr, A. Kazda, D. Zhuk. Small Promise CSPs reducing to large CSPs. Log. Methods Comput. Sci. 18, no. 3, Paper No. 25, 14 pp, 2022. [pdf]
  5. P. Mayr, A. Szendrei. Algebras from congruences. Algebra Universalis 82 (2021), no. 4, Paper No. 55, 39 pp. [pdf]
  6. G. Deng, E. El Sai, T. Manders, P. Mayr, P. Nakkirt, A. Sparks. Sandwiches for promise constraint satisfaction. Algebra Universalis 82 (2021), no. 1, Paper No. 15, 8 pp. [pdf]
  7. W. DeMeo, P. Mayr, N. Ruskuc. Bounded homomorphisms and finitely generated fiber products of lattices. Internat. J. Algebra Comput. 30 (2020), no. 4, 693–710. [pdf]
  8. P. Mayr, N. Ruskuc, Presentations for subrings and subalgebras of finite co-rank. Q. J. Math. 71 (2020), no. 1, 53–71. [pdf]
  9. P. Mayr, N. Ruskuc, Generating subdirect products. Journal London Math. Soc., 100(2), 404-424, 2019. [pdf]
  10. A. Bulatov, P. Mayr, A. Szendrei, The subpower membership problem for finite algebras with cube terms. Logical Methods in Computer Science, February 13, 2019, Volume 15, Issue 1 [pdf]
  11. K. Kearnes, P. Mayr, N. Ruskuc, Solvable quotients of subdirect products of perfect groups are nilpotent. Bulletin London Math. Society 50 (2018), no. 6, 1016-1026. [pdf]
  12. P. Mayr, N. Ruskuc, Finiteness properties of direct products of algebraic structures. J. Algebra 494 (2018), 167-187. [pdf]
  13. A. Bulatov, M. Kozik, P. Mayr, M. Steindl, The subpower membership problem for semigroups. Internat. J. Algebra Comput. 26, no. 7, 1435-1451, 2016. [pdf]
  14. H. Chen, P. Mayr, Quantified Constraint Satisfaction on monoids. 25th EACSL Annual Conference on Computer Science Logic (CSL 2016), Jean-Marc Talbot and Laurent Regnier (Eds.), LIPICS Vol. 62, 2016. [pdf]
  15. E. Aichinger, P. Mayr, Finitely generated equational classes. Journal Pure and Applied Algebra, 220, 2816-2827, 2016. [pdf]
  16. E. Aichinger, P. Mayr. Independence of algebras with edge term. Internat. J. Algebra Comput. (IJAC) 25(7), 1145-1157, 2015. [pdf]
  17. E. Aichinger, P. Mayr, R. McKenzie. On the number of finite algebraic structures. Journal European Math. Society (JEMS), 16(8), 1673-1686, 2014. [pdf]
  18. W. Bentz, P. Mayr. Supernilpotence prevents dualizablility. Journal Australian Math. Society, 96, 1--24, 2014. [pdf]
  19. P. Mayr. On finitely related semigroups. Semigroup Forum, 86(3), 613--633, 2013.
  20. P. Mayr. The subpower membership problem for Mal'cev algebras. International Journal of Algebra and Computation (IJAC), 22(7), 1250075 (23 pages), 2012.
  21. G. Horvath, P. Mayr, A. Pongracz. Characterizing translations on groups by cosets of their subgroups. Comm. Algebra, 40, 3141--3168, 2012.
  22. E. Aichinger, P. Mayr, J. D. P. Meldrum, G. L. Peterson and S. D. Scott. Units of compatible nearrings. Monatsh. Math., 164(2), 119--132, 2011.
  23. P. Mayr. Mal'cev algebras with supernilpotent centralizers. Algebra Universalis, 65(2), 193--211, 2011.
  24. K. Kaarli, P. Mayr. Polynomial functions on subdirect products. Monatsh. Math., 159(4), 341--359, 2010.
  25. E. Jabara, P. Mayr. Frobenius complements of exponent dividing 2^m*9. Forum Math., 21(2), 217--220, 2009.
  26. P. Mayr. Polynomial functions on squarefree groups. International Journal of Algebra and Computation (IJAC), 18(4), 759--777, 2008.
  27. G. Landsmann, P. Mayr, J. Schicho. A topological property of polynomial functions on GL(2,R). Aequationes Math., 73(1-2), 71--77, 2007.
  28. E. Aichinger, P. Mayr. Polynomial clones on groups of order $pq$. Acta Math. Hungar., 114(3), 267--285, 2007.
  29. P. Mayr. The polynomial functions on Frobenius complements. Acta Sci. Math. (Szeged), 72(1-2), 37--50, 2006.
  30. P. Mayr. Sharply 2-transitive groups with point stabilizer of exponent 3 or 6. Proc. Amer. Math. Soc., 134(1), 9--13, 2006.
  31. T. Boykett, P. Mayr. Fixed-point-free automorphism groups from rings. Southeast Asian Bull. Math., 29(2), 253--257, 2005.
  32. T. Boykett, P. Mayr.. Difference methods and Ferrero pairs. In Kiechle, Hubert (ed.) et al., Nearrings and nearfields. Proceedings of the conference on nearrings and nearfields, Hamburg, Germany, July 27-August 3, 2003. Dordrecht: Springer, 177--187, 2005.
  33. E. Aichinger, P Mayr. Polynomial functions and endomorphism near-rings on certain linear groups. Comm. Algebra, 31(11), 5627--5651, 2003.
  34. P. Mayr, F. Morini. Nearrings whose set of {$N$-subgroups is linearly ordered. Results Math., 42(3-4), 339--348, 2002.
  35. F. Binder, P. Mayr. Algorithms for finite near-rings and their N-groups. J. Symbolic Comput., 32(1-2), 23--38, 2001.
  36. E. Aichinger, F. Binder, J. Ecker, P. Mayr, C. Nöbauer. Algorithms for near-rings of non-linear transformations. Proceedings of the ISSAC 2000, 23--29, St. Andrews, Scotland, ACM, 2000.

Software

E. Aichinger, F. Binder, J. Ecker, P. Mayr, C. Nöbauer. SONATA (GAP package for computation with nearrings), version 2.9 (2018).