Julian Brough

activity

20152017

collaborators

5 papers

math.GR2017

On vanishing class sizes in finite groups

Mariagrazia Bianchi, Julian M. A. Brough, Rachel D. Camina +1

Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $χ$ of $G$ such that $χ (g) = 0$ ; in this case, we say that t…

math.GR2017

On vanishing criteria that control finite group structure II

Julian Brough, Qingjun Kong

In a paper by the first author it was shown that for certain arithmetical results on conjugacy class sizes it is enough to only consider the vanishing conjugacy class sizes. In thi…

math.GR2017

Central intersections of element centralisers

Julian Brough

In 1970 R. Schmidt gave a structural classification for CA-groups. In this paper we consider a condition upon the intersection of element centralisers which turns out to be equival…

math.GR2016

Non-vanishing elements in finite groups

Julian Brough

Many results have been established about determining whether or not an element evaluates to zero on an irreducible character of a group. In this note it is shown that if a group $G…

math.GR2015

A criteria for a finite permutation group to be transitive

Julian Brough

Let $G$ be a finite permutation group on a finite set $Ω$ . The notion of $G$ being quasi-transitive on $Ω$ was defined by Alan Camina \cite{Camina}; in that paper conditions were e…