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:

- The design and analysis of algorithms for computing with invariant relations of algebras and their applications to Constraint Satisfaction Problems CSP (with A. Bulatov, A. Szendrei, et al).
- The characterization of finite algebras that are finitely related, i.e., whose sets of term functions are determined by finitely many relations. All algebras with edge term (a generalization of a group operation) are finitely related (with E. Aichinger, R. McKenzie, 2014), some (but not on all) semigroups are finitely related (2013).
- Every subvariety of a finitely generated equational class with edge term is finitely generated (with E. Aichinger, 2015).

- P. Mayr and N. Ruskuc,
*Presentations for subrings and subalgebras of finite co-rank.*Submitted 2017. [pdf] - P. Mayr and N. Ruskuc,
*Finiteness properties of direct products of algebraic structures.*J. Algebra 494 (2018), 167-187. [pdf] -
A. Bulatov, M. Kozik, P. Mayr, and M. Steindl,
*The subpower membership problem for semigroups.*Internat. J. Algebra Comput. 26, no. 7, 1435-1451, 2016. [pdf] -
H. Chen and 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] -
E. Aichinger and P. Mayr,
*Finitely generated equational classes.*Journal Pure and Applied Algebra, 220, 2816--2827, 2016. [pdf] -
E. Aichinger and P. Mayr.
*Independence of algebras with edge term.*Internat. J. Algebra Comput. (IJAC) 25(7), 1145–1157, 2015. [pdf] -
E. Aichinger, P. Mayr and R. McKenzie.
*On the number of finite algebraic structures.*Journal European Math. Society (JEMS), 16(8), 1673--1686, 2014. [pdf] -
W. Bentz and P. Mayr.
*Supernilpotence prevents dualizablility.*Journal Australian Math. Society, 96, 1--24, 2014. [pdf] -
P. Mayr.
*On finitely related semigroups.*Semigroup Forum, 86(3), 613--633, 2013. -
P. Mayr.
*The subpower membership problem for Mal'cev algebras.*International Journal of Algebra and Computation (IJAC), 22(7), 1250075 (23 pages), 2012. -
G. Horvath, P. Mayr, and A. Pongracz.
*Characterizing translations on groups by cosets of their subgroups.*Comm. Algebra, 40, 3141--3168, 2012. -
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. -
P. Mayr.
*Mal'cev algebras with supernilpotent centralizers.*Algebra Universalis, 65(2), 193--211, 2011. -
K. Kaarli and P. Mayr.
*Polynomial functions on subdirect products.*Monatsh. Math., 159(4), 341--359, 2010. -
E. Jabara and P. Mayr.
*Frobenius complements of exponent dividing 2^m*9.*Forum Math., 21(2), 217--220, 2009. -
P. Mayr.
*Polynomial functions on squarefree groups.*International Journal of Algebra and Computation (IJAC), 18(4), 759--777, 2008. -
G. Landsmann, P. Mayr and J. Schicho.
*A topological property of polynomial functions on GL(2,R).*Aequationes Math., 73(1-2), 71--77, 2007. -
E. Aichinger and P. Mayr.
*Polynomial clones on groups of order $pq$.*Acta Math. Hungar., 114(3), 267--285, 2007. -
P. Mayr.
*The polynomial functions on Frobenius complements.*Acta Sci. Math. (Szeged), 72(1-2), 37--50, 2006. -
P. Mayr.
*Sharply 2-transitive groups with point stabilizer of exponent 3 or 6.*Proc. Amer. Math. Soc., 134(1), 9--13, 2006. -
T. Boykett and P. Mayr.
*Fixed-point-free automorphism groups from rings.*Southeast Asian Bull. Math., 29(2), 253--257, 2005. -
T. Boykett and 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. -
E. Aichinger and P Mayr.
*Polynomial functions and endomorphism near-rings on certain linear groups.*Comm. Algebra, 31(11), 5627--5651, 2003. -
P. Mayr and F. Morini.
*Nearrings whose set of {$N$*-subgroups is linearly ordered. Results Math., 42(3-4), 339--348, 2002. -
F. Binder and P. Mayr.
*Algorithms for finite near-rings and their N-groups.*J. Symbolic Comput., 32(1-2), 23--38, 2001. -
E. Aichinger, F. Binder, J. Ecker, P. Mayr and C. Nöbauer.
*Algorithms for near-rings of non-linear transformations.*Proceedings of the ISSAC 2000, 23--29, St. Andrews, Scotland, ACM, 2000.