A description of a class of finite semigroups that are near to being Malcev nilpotent

In this paper we continue the investigations on the algebraic structure of a finite semigroup $S$ that is determined by its associated upper non-nilpotent graph $\mathcal{N}_{S}$. The vertices of this graph are the elements of $S$ and two vertices are adjacent if they generate a semigroup that is not nilpotent (in the sense of Malcev). We introduce a class of semigroups in which the Mal'cev nilpotent property lifts through ideal chains. We call this the class of \B\ semigroups. The definition is such that the global information that a semigroup is not nilpotent induces local information, i.e. some two-generated subsemigroups are not nilpotent. It turns out that a finite monoid (in particular, a finite group) is \B\ if and only if it is nilpotent. Our main result is a description of \B\ finite semigroups $S$ in terms of their associated graph ${\mathcal N}_{S}$. In particular, $S$ has a largest nilpotent ideal, say $K$, and $S/K$ is a 0-disjoint union of its connected components (adjoined with a zero) with at least two elements

Finite nilpotent semigroups of small coclass

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are classified. Presentations for all such semigroups and formulae for their numbers are obtained. The classification is provided up to isomorphism as well as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups are identified within the classification.Comment: 11 page

On the Representation Theory of Negative Spin

We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive and negative representations with the help of generalized characters and write down explicit reduction formulae for the products. From the characters, we define effective dimensions for the negative spin representations, find that they are fractional, and point out that the dimensions behave consistently under multiplication and decomposition of representations.Comment: 21 pages, no figures, Latex2

Советские диссиденты в Италии

Dalla meta degli anni Settanta l’Italia cominciò a conoscere la lettura russa dello Samizdat ma la sua ricezione fu difficile a causa della dominante cultura di sinistra, la quale era diffidente nei confronti delle opposizioni all’interno dell’URSS. Un’eccezione fu la Biennale di Venezia del 1977, dedicata ai dissidenti dell’Est Europa. С середины 1970-х гг. Италия стала знакомиться с русской диссидентской и самиздатовской литературой, однако ее восприятие было затруднено доминировавшей тогда левой культурой, недоверчиво относившейся к оппозиции внутри СССР. Одним из исключений той эпохи стала Венецианская Бьеннале 1977 г., посвященная теме инакомыслия в Восточной Европе.

Geometry of Reidemeister classes and twisted Burnside theorem

This is a (mostly expository) paper on Reidemeister classes, twisted Burnside-Frobenius theory, congruences, R-infinity property and all that. It was written in 2005 and published in 2008. We post it as it was, only the bibliography data is updated. For some of the recent progress see e.g. arXiv:0903.4533, arXiv:0903.3455, arXiv:0802.2937, arXiv:0712.2601, arXiv:0704.3411, arXiv:math/0703744, arXiv:math/0606725, arXiv:math/0606764, arXiv:0805.1371 and references there

On conjugacy separability of fibre products

In this paper we study conjugacy separability of subdirect products of two free (or hyperbolic) groups. We establish necessary and sufficient criteria and apply them to fibre products to produce a finitely presented group $G_1$ in which all finite index subgroups are conjugacy separable, but which has an index $2$ overgroup that is not conjugacy separable. Conversely, we construct a finitely presented group $G_2$ which has a non-conjugacy separable subgroup of index $2$ such that every finite index normal overgroup of $G_2$ is conjugacy separable. The normality of the overgroup is essential in the last example, as such a group $G_2$ will always posses an index $3$ overgroup that is not conjugacy separable. Finally, we characterize $p$-conjugacy separable subdirect products of two free groups, where $p$ is a prime. We show that fibre products provide a natural correspondence between residually finite $p$-groups and $p$-conjugacy separable subdirect products of two non-abelian free groups. As a consequence, we deduce that the open question about the existence of an infinite finitely presented residually finite $p$-group is equivalent to the question about the existence of a finitely generated $p$-conjugacy separable full subdirect product of infinite index in the direct product of two free groups.Comment: v2: 38 pages; this is the version accepted for publicatio

Cohomology and Decomposition of Tensor Product Representations of SL(2,R)

We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit decomposition formulae, true modulo a natural cohomological reduction, for the tensor products.Comment: 22 pages, no figures, Latex2e Added section on product of finite and continuous serie

Усовершенствование вспомогательных опор станочных приспособлений

Допоміжна підвідна опора містить корпус із опорним штирем, що опирається своїм скосом на похилу поверхню клина, стрижень з головкою, що вкручений в глухий нарізний отвір клина, і пружину стиску, що контактує з клином. Кнопка із ступінчастим отвором має можливість переміщатися співвісно зі стрижнем. Поворотна опора може змінювати кут свого нахилу.Вспомогательная подводимая опора содержит корпус с опорным штырем, который опирается своим скосом на наклонную поверхность клина, стержень с головкой, вкрученный в глухое резьбовое отверстие клина, и пружину сжатия, контактирующую с клином. Кнопка со ступенчатым отверстием имеет возможность перемещаться соосно со стержнем. Поворотная опора может изменять угол своего наклона.An auxiliary underpinning support comprises a body with a support pin, which is based by its slant on an inclined surface of a wedge, a rod with a head is screwed into a blind threaded hole of the wedge, and a compression spring in contact with the wedge. Button with stepped bore can move axially with the rod. Rotary support can change its angle of inclination