Related papers: Limit varieties generated by finite non-J-trivial …
A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…
It is proved that every finitely subdirectly irreducible De Morgan monoid A (with neutral element e) is either (i) a Sugihara chain in which e covers not(e) or (ii) the union of an interval subalgebra [not(a), a] and two chains of…
We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation…
We observe that for each $n\ge 2$, the identities of the stylic monoid with $n$ generators coincide with the identities of $n$-generated monoids from other distinguished series of $\mathscr{J}$-trivial monoids studied in the literature,…
We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The first of them indicates a countably infinite family of…
It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a…
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the…
Let $G$ be a finite almost simple group. It is well known that $G$ can be generated by 3 elements, and in previous work we showed that 6 generators suffice for all maximal subgroups of $G$. In this paper we consider subgroups at the next…
We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based finite $\mathcal{R}$-trivial semigroup. This provides unified…
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite…
It is unknown so far, whether the lattice of all varieties of monoids satisfies some non-trivial identity. The objective of this note is to give the negative answer to this question. Namely, we prove that any finite lattice is a homomorphic…
The variety DA of finite monoids has a huge number of different characterizations, ranging from two-variable first-order logic FO^2 to unambiguous polynomials. In order to study the structure of the subvarieties of DA, Trotter and Weil…
A slight modification of the definition of the Thompson-Higman groups G_k1 and F_k1 leads to inverse monoids that map onto G_k1 (respectively F_k1), and that have interesting properties: they are finitely generated, and residually finite.…
We completely classify all varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive.
We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating…
Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.
We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.
Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R^3. It is shown that the unknot with maximal Thurston--Bennequin invariant of -1 has a unique linear-quadratic at infinity generating family,…