Related papers: Groups with a small average number of zeros in the…
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.
There has been some interest on how the average character degree affects the structure of a finite group. We define, and denote by $ \mathrm{anz}(G) $, the average number of zeros of characters of a finite group $ G $ as the number of zeros…
We provide an example of a finite group with a conjugacy class of average size on which fewer than half of the irreducible characters are either zero or a root of unity.
The average order of a finite group G is denoted by o(G). In this note, we classify groups whose average orders are less than o(S4), where S4 is the symmetric group on four elements. Moreover, we prove that G \cong S4 if and only if o(G) =…
Finite groups with very few character values are characterized. The following is the main result of this article: a finite non-abelian group has precisely four character values if and only if it is the generalized dihedral group of a…
A classical theorem on character degrees states that if a finite group has fewer than four character degrees, then the group is solvable. We prove a corresponding result on character values by showing that if a finite group has fewer than…
Computations of Miller and Scheinerman suggest that the vast majority of the zeros appearing in the character table of the symmetric group are of a certain special type. While we cannot prove this, we resolve a conjecture arising in their…
We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
In this note, we study the finite groups with the number of cylic subgroups no greater than 6.
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of…
In this paper, we classify the finite simple groups with an abelian Sylow subgroup.
We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.
We classify all of the groups with twelve or fewer subgroups. This paper is the proof of the entries in a submission to the Online Encyclopedia of Integer Sequences.
We classify finite non-solvable groups with a faithful primitive irreducible complex character that vanishes on a unique conjugacy class. Our results answer a question of Dixon and Rahnamai Barghi and suggest an extension of Burnside's…
A supercharacter theory for a finite group $G$ is a set of superclasses each of which is a union of conjugacy classes together with a set of sums of irreducible characters called supercharacters that together satisfy certain compatibility…
We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.
It is shown that the classification theorems for semisimple algebraic groups in characteristic zero can be derived quite simply and naturally from the corresponding theorems for Lie algebras by using a little of the theory of tensor…