1,092 research outputs found
On the (un)decidability of a near-unanimity term
We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present partial results towards proving the decidability of the general problem
Semilattices with a group of automorphisms
We investigate semilattices expanded by a group F of automorphisms
acting as new unary basic operations. We describe up to isomorphism all
simple algebras of this kind in case that F is commutative. Finally, we present
an example of a simple algebra that does not fit in the previous description,
if F is not commutative
On the number of conjugacy classes of a permutation group
We prove that any permutation group of degree has at most
conjugacy classes.Comment: 9 page
The minimal base size for a p-solvable linear group
Let be a finite vector space over a finite field of order and of
characteristic . Let be a -solvable completely reducible
linear group. Then there exists a base for on of size at most
unless in which case there exists a base of size at most . The
first statement extends a recent result of Halasi and Podoski and the second
statement generalizes a theorem of Seress. An extension of a theorem of P\'alfy
and Wolf is also given.Comment: 11 page
Quasiequational Theories of Flat Algebras
We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely q-based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely q-based
The endomorphism semiring of a semilattice
We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element
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