The Bergman property for endomorphism monoids of some Fraïssé limits
Abstract
Based on an idea of Y. Péresse and some results of Maltcev, Mitchell and Ruškuc, we present sufficient conditions under which the endomorphism monoid of a countably infinite ultrahomogeneous first-order structure has the Bergman property. This property has played a prominent role both in the theory of infinite permutation groups and, more recently, in semigroup theory. As a byproduct of our considerations, we establish a criterion for a countably infinite ultrahomogeneous structure to be homomorphism-homogeneous.
Funding source: Ministry of Science and Technological Development of the Republic of Serbia
Award Identifier / Grant number: 174019
The author is indebted a great deal to an anonymous referee whose thorough reading of the initial manuscript substantially improved the presentation of the results. I am also very grateful to James D. Mitchell, Nik Ruškuc (University of St Andrews) and Dragan Mašulović (University of Novi Sad) for valuable discussions and correspondence concerning the topic of this note.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Centralizer of an idempotent in a reductive monoid
- Free subgroups within the images of quantum representations
- The Bergman property for endomorphism monoids of some Fraïssé limits
- Boundary value problems for heat equation with certain potentials in Lipschitz cylinders
- On some multiplicity and mixed multiplicity formulas
- Free group algebras in Malcev–Neumann skew fields of fractions
- Decomposition theorems for QK spaces and applications
- Ideals of generalized invariants, local cohomology and Macaulay's double duality theorem
- The distribution of the logarithm in an orthogonal and a symplectic family of L-functions
- On seven-dimensional quaternionic contact solvable Lie groups
- Weitzenböck derivations of nilpotency 3
- Unital associahedra
- On the norm of the Lp-Fourier transform on compact extensions of ℝn
- On the existence of semifields of order q8 admitting elementary abelian groups of order 8
Articles in the same Issue
- Frontmatter
- Centralizer of an idempotent in a reductive monoid
- Free subgroups within the images of quantum representations
- The Bergman property for endomorphism monoids of some Fraïssé limits
- Boundary value problems for heat equation with certain potentials in Lipschitz cylinders
- On some multiplicity and mixed multiplicity formulas
- Free group algebras in Malcev–Neumann skew fields of fractions
- Decomposition theorems for QK spaces and applications
- Ideals of generalized invariants, local cohomology and Macaulay's double duality theorem
- The distribution of the logarithm in an orthogonal and a symplectic family of L-functions
- On seven-dimensional quaternionic contact solvable Lie groups
- Weitzenböck derivations of nilpotency 3
- Unital associahedra
- On the norm of the Lp-Fourier transform on compact extensions of ℝn
- On the existence of semifields of order q8 admitting elementary abelian groups of order 8
