相关论文: Principal blocks with six ordinary irreducible cha…

It is proved that a profinite group $G$ has fewer than $2^{\aleph_0}$ conjugacy classes of $p$-elements for an odd prime $p$ if and only if its $p$-Sylow subgroups are finite. (Here, by a $p$-element one understands an element that either…

In this paper, we calculate the numbers of irreducible ordinary characters and irreducible Brauer characters in a block of a finite group $G$, whose associated fusion system over a 2-subgroup $P$ of $G$ (which is a defect group of the…

In this note, we determine the irreducible characters for the simple algebraic groups of type $A_5$ over an algebraically closed field $K$ of characteristic 3, by using a theorem of Xi Nanhua and the Matlab software. In order to obtain…

Given a generalized $e$-block $B$ of a symmetric group and an $e$-regular conjugacy class $C$, we study the number of irreducible characters in $B$ which do not vanish on $C$ and find lower bounds for it.

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 exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.

A pointed $p$-group is a pointed group $P_\gamma$ such that $P$ is a $p$-group. We parameterize the pointed $p$-groups on a group algebra or on a block algebra of a group algebra. The parameterization involves $p$-subgroups and irreducible…

Let $ G$ be a finite group and $p$ be a prime. Let $ \mathrm{Vo}(G) $ denote the set of the orders of vanishing elements, $\mathrm{Vo}_{p} (G)$ be the subset of $ \mathrm{Vo}(G) $ consisting of those orders of vanishing elements divisible…

In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of $ 25 $ carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown that $ 4 $ unipotent Sylow subgroups suffice. We prove that…

We determine the character tables of Sylow $p$-subgroups $U$ of the Steinberg triality groups ${^3}D_4(q^3)$, where $q$ is a power of an odd prime $p$.

We enumerate the number of complex irreducible representations of each degree of general unitary groups of degree 4 over principal ideal rings of length 2.

We consider sequences of degrees of ordinary irreducible $S_n$-characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of $n$ with leading coefficient less than one. We show that any…

Denote by $\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $\nu_p(H)\leq\nu_p(G)$ for $H\leq G$, however $\nu_p(H)$ does not divide $\nu_p(G)$ in general. In this paper we reduce the question whether…

An irreducible ordinary character of a finite reductive group is called quadratic unipotent if it corresponds under Jordan decomposition to a semisimple element $s$ in a dual group such that $s^2=1$. We prove that there is a bijection…

Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and…

We classify all finite groups $G$ which possesses an element $x\in G$ such that every irreducible character of $G$ takes a root of unity value at $x$.

In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special…

We show that a group is a GVZ-group if and only if it is a flat group. We show that the nilpotence class of a GVZ-group is bounded by the number of distinct degrees of irreducible characters. We also show that certain CM-groups can be…

It has been conjectured that if the number of distinct irreducible constituents of the product of two faithful irreducible characters of a finite $p$-group, for $p\geq5$, is bigger than $(p+1)/2$, then it is at least $p$. We give a…