Constructing the Irreducible Characters of J4 with GAP

On Finite Groups With Two Irreducible Character Degrees

On the irreducible characters of Camina triples

The Camina triple condition is a generalization of the Camina condition in the theory of finite groups. The irreducible characters of Camina triples have been verified in the some special cases. In this paper, we consider a Camina triple (G,M,N)  and determine the irreducible characters of G in terms of the irreducible characters of M and G/N.  

Irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$

‎‎Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

Some connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups

‎Let $G$ be a finite group‎. ‎We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$‎. ‎In this paper we characterize solvable groups $G$ in which the derived covering number is finite‎.‎ 

A New Existence Proof of Janko’s Simple Group

Janko’s large simple sporadic group J4 was originally constructed by Benson, Conway, Norton, Parker and Thackray as a subgroup of the general linear group GL112(2) of all invertible 112× 112-matrices over the field GF (2) with 2 elements, see [1] and [13]. So far the construction of the 112-dimensional 2-modular irreducible representation of J4 is only described in Benson’s thesis [1] at Cambri...