J. Cossey

activity

20062026

most citedConstructing all irreducible Specht modules in a block of the symmetric group

3 citations · 5 across the 8 of their papers we have counts for

collaborators

10 papers

math.GR2026

A height-zero type result for blocks of solvable groups

James P. Cossey

Let $B$ be a $p$ -block of a finite group $G$ with defect group $D$ . The more difficult direction of the recently proven height zero conjecture says that $D$ is abelian if every cha…

math.GR2025

Sylow subgroups and the number of irreducible characters of degrees divisible by a prime $p$

James P. Cossey, Mark L. Lewis, A. A. Schaeffer Fry +1

Let $G$ be a finite group and $p$ a prime. We establish an upper bound for the derived length of a Sylow $p$ -subgroup of $G$ in terms of the number of irreducible characters of $G$ …

math.GR2014

On a conjecture of Gluck

James P. Cossey, Zoltán Halasi, Attila Maróti +1

Let $F (G)$ and $b (G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$ . A well-known conjecture of D. Gluck…

math.GR2013

Controlling composition factors of a finite group by its character degree ratio

James P. Cossey, Hung Ngoc Nguyen

For a finite nonabelian group $G$ let $\rat(G)$ be the largest ratio of degrees of two nonlinear irreducible characters of $G$ . We show that nonabelian composition factors of $G$ a…

math.GR2011

Counting characters in blocks of solvable groups with abelian defect group

James P. Cossey, Mark L. Lewis

If $G$ is a solvable group and $p$ is a prime, then the Fong-Swan theorem shows that given any irreducible Brauer character $ϕ$ of $G$ , there exists a character $χ\in \irrg$ such t…

math.GR2010

Lifts and vertex pairs in solvable groups