In a paper from 1980, Shelah constructed an uncountable group all of whose proper
subgroups are countable. Assuming the continuum hypothesis, he constructed an …

We give a complete description of the congruences on the partition monoid $ P_X $ and the
partial Brauer monoid $ PB_X $, where $ X $ is an arbitrary infinite set, and also of the …

We develop a theory of Katětov functors which provide a uniform way of constructing Fraïssé
limits. Among applications, we present short proofs and improvements of several recent …

Let 𝒫X and 𝒮X be the partition monoid and symmetric group on an infinite set X. We show
that 𝒫X may be generated by 𝒮X together with two (but no fewer) additional partitions, and …

We study monoids generated by various combinations of idempotents and one-or two-sided
units of an infinite partial Brauer monoid. This yields a total of eight such monoids, each with …

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 …

Transformation monoids carry a canonical topology—the topology of point-wise
convergence. A closed transformation monoid MM is said to have automatic …

We prove that any countable set of surjective functions on an infinite set of cardinality ℵn
with n∈ N can be generated by at most n2/2+ 9n/2+ 7 surjective functions of the same set; …

We investigate the generation of factorizable inverse monoids, paying special attention to
the factorizable parts of the symmetric and dual symmetric inverse monoids. Key ideas …

For a monoid M, we denote by G (M) the group of units, E (M) the submonoid generated by
the idempotents, and GL (M) and GR (M) the submonoids consisting of all left or right units …