‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if G is an M -group with odd order, then every irreducible character is super monomial. We prove that the conjecture is true if G is an M -group of odd order where every irreducible character is a {p}-lift for some prime p. We say that a group where irreducible cha...

The character table of the fully nonrigid water cluster (cyclic forms), (H_{2}O){_i}, with C{_ih} symmetry derived for the first time, for 2<=i <=6. The group of all feasible permutations is the wreath product of groups S{_i}[S{_2}] which consists of i!2i operations for i = 2, ..., 6 divided into ( w.r.t) 5, 10, 20, 36, 65 conjugacy classes and 5, 10, 20, 36, 65 irreducible representations resp...

We study Shintani lifting of real-valued irreducible characters of finite reductive groups. In particular, if G is a connected reductive group defined over Fq, and ψ is an irreducible character of G(Fqm) which is the lift of an irreducible character χ of G(Fq), we prove ψ is real-valued if and only if χ is real-valued. In the case m = 2, we show that if χ is invariant under the twisting operato...

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ‎${f_4(2)}.$‎

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...

Kriegel's self-representationalist (SR) theory of phenomenal consciousness pursues two projects. The first is to offer a positive account of how conscious experience arises from physical brain processes. The second is to explain why consciousness misleadingly appears to be irreducible to the physical i.e. to 'demystify' consciousness. This paper seeks to determine whether SR succeeds on the sec...