Related papers: Vanishing-off subgroups and supercharacter theory …

The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.

The deep theory of approximate subgroups establishes 3-step product growth for subsets of finite simple groups $G$ of Lie type of bounded rank. In this paper we obtain 2-step growth results for representations of such groups $G$ (including…

Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$,…

We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…

We analyse the subgroup structure of direct products of groups. Earlier work on this topic has revealed that higher finiteness properties play a crucial role in determining which groups appear as subgroups of direct products of free groups…

Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question…

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…

For a star-shaped graph, we introduce special characters and study their properties. We decompose special characters into odd and even parts and study their evolution under reflections. We apply the obtained formulas to prove that the…

We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to…

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups. Finally, we show a specific family of graphs cannot occur…

In this paper we study probabilistic aspects such as subgroup commutativity degree and cyclic subgroup commutativity degree of the (generalized) dicyclic groups. We find explicit formulas for these concepts and we provide another example of…

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more…

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each…

We give an $AB$-factorization of the supercharacter table of the group of $n\times n$ unipotent upper triangular matrices over $\FF_q$, where $A$ is a lower-triangular matrix with entries in $\ZZ[q]$ and $B$ is a unipotent upper-triangular…

We study fundamental forms of algebraic varieties using the sheaves of principal parts of line bundles and establish a vanishing theorem for any order fundamental forms. We also give connection of fundamental forms with the higher order…

We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.

In this paper, we study some variations of the well-known It\^{o}-Michler theorem for $p$-Brauer characters using various inequalities involving the $p$-Brauer character degrees of finite groups. Several new criteria for the existence of a…

If a group $G$ is $\pi$-separable, where $\pi$ is a set of primes, the set of irreducible characters $\operatorname{B}_{\pi}(G) \cup \operatorname{B}_{\pi'}(G)$ can be defined. In this paper, we prove that there are variants of some…