


September 14, 2017

All participants




November 2, 2017

A. Savchuk


On transformation semigroups based on digraphs, III




November 9, 2017

A. Savchuk


On transformation semigroups based on digraphs, IV




November 23, 2017

A. Savchuk


On transformation semigroups based on digraphs, V




November 30, 2017

P. Khylynskyi
 



December 7, 2017

P. Khylynskyi
 



December 19, 2017

All participants




December 28, 2017

A. Ravsky


Two new algebra working problems



April 17, 2018

O. Gutik


On group congruences of inverse semigroups whose contain the semigroup of partial cofinite isometries of positive integers, III

Let $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ be the the semigroup of cofinite monotone partial
bijections of the set of pusitive integers $\mathbb{N}$ and $\mathbf{I}\mathbb{N}_{\infty}$ be the semigroup of all partial cofinite isometries of $\mathbb{N}$. We give a criterium when
an inverse subsemigroup $S$ of $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}$ has the following property: every nonidentity
congruence of $S$ is a group congrunce. We describe minimal inviverse subsemigroups with such property.



April 25, 2018

O. Gutik


On variants of the bicyclic extended semigroup

We describe the group $\mathbf{Aut}\left(\mathcal{C}_{\mathbb{Z}}\right)$ of automorphisms of the extended bicyclic semigroup $\mathcal{C}_{\mathbb{Z}}$ and study variants
$\mathcal{C}_{\mathbb{Z}}^{m,n}$ of the extended bicycle semigroup $\mathcal{C}_{\mathbb{Z}}$, where $m,n\in\mathbb{Z}$. Especially we prove that
$\mathbf{Aut}\left(\mathcal{C}_{\mathbb{Z}}\right)$ is isomorphic to the additive group of integers and describe the subset of idempotents $E(\mathcal{C}_{\mathbb{Z}}^{m,n})$ and Green's
relations of the semigroup $\mathcal{C}_{\mathbb{Z}}^{m,n}$. Also we show that $E(\mathcal{C}_{\mathbb{Z}}^{m,n})$ is an $\omega$chain and any two variants of the extended bicyclic
semigroup $\mathcal{C}_{\mathbb{Z}}$ are isomorphic.



