Related papers: On the unit groups of partial Burnside rings

It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We…

For a saturated fusion system $\mathcal F$ on a $p$-group $S$, we study the Burnside ring of the fusion system $B(\mathcal F)$, as defined by Matthew Gelvin and Sune Reeh, which is a subring of the Burnside ring $B(S)$. We give criteria for…

All groups have 2 generators. For every prime power q, the Generalized Burnside Theorem (Theorem GB) produces an infinite number of solvable groups, Some, such as groups of a prime power exponent, have only elements of finite order and are…

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

For a perfectoid ring $R$ and a natural number $n$ we investigate the essential image of the category of truncated by $n$ Barsotti-Tate groups under the anti-equivalence between commutative, finite, locally free, $R$-group schemes of…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.

In this note we present an algorithm for the construction of the unit group of the Burnside ring $\Omega(G)$ of a finite group $G$ from a list of representatives of the conjugacy classes of subgroups of G.

In this note we give a generalization of the well-known Menon's identity. This is based on applying the Burnside's lemma to a certain group action.

After we have given a survey on the Burnside ring of a finite group, we discuss and analyze various extensions of this notion to infinite (discrete) groups. The first three are the finite-G-set-version, the inverse-limit-version and the…

In his seminal paper on complex reflection arrangements, Bessis introduces a Garside structure for the braid group of a well-generated irreducible complex reflection group. Using this Garside structure, he establishes a strong connection…

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…

This paper stresses the strong link between the existence of partial holomorphic connections on the normal bundle of a foliation seen as a quotient of the ambient tangent bundle and the extendability of a foliation to an infinitesimal…

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…

We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…

In a pair of recent papers (one to appear and one forthcoming), the author develops a general version of small cancellation theory applicable in higher dimensions, and then applies this theory to the Burnside groups of sufficiently large…

For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finite-dimensional fixed points of the induced map f^…

We approach celebrated theorems of Burnside and Wedderburn via simultaneous triangularization. First, for a general field $F$, we prove that $M_n(F)$ is the only irrreducible subalgebra of triangularizable matrices in $M_n(F)$ provided such…