J. W. MacQuarrie

activity

20212026

collaborators

7 papers

math.RT2026

Finiteness properties of profinite blocks and blocks with defect group $Z_{p}^{n}$

Florian Eisele, John W. MacQuarrie

We prove that any block of a profinite group with a topologically finitely generated defect group $D$ is isomorphic to a block of a virtually pro- $p$ group, and if $D$ is finitely…

math.GR2025

The profinite genus of the groups $Z^{n} ⋊ C_{p^{2}}$

Marlon Estanislau, John MacQuarrie, Anderson Porto

A formula is given for the profinite genus of groups of the form $Z^{n} ⋊ C_{p^{2}}$ , completing the calculation of the size of the genus of semidirect products of the f…

math.RT2025

Block pro-fusion systems for profinite groups and blocks with infinite dihedral defect groups

Florian Eisele, Ricardo J. Franquiz Flores, John W. MacQuarrie

We introduce block pro-fusion systems for blocks of profinite groups, prove a profinite version of Puig's structure theorem for nilpotent blocks, and use it to show that there is o…

math.RT2024

Projective resolutions of simple modules and Hochschild cohomology for incidence algebras

Viktor Bekkert, John William MacQuarrie, Júlio Marques

We give a practical, algorithmic method to calculate minimal projective resolutions of simple modules for a finite dimensional incidence $k$ -algebra $Λ$ , where $k$ is a field. We a…

math.RT2022

Butler's Method applied to $Z_{p} [C_{p} \times C_{p}]$ -permutation modules

John MacQuarrie, Marlon Stefano

Let $G$ be a finite $p$ -group with normal subgroup $N$ of order $p$ . The first author and Zalesskii have previously given a characterization of permutation modules for $\mathbb{Z}_…

math.KT2021

Homological properties of extensions of algebras

Kostiantyn Iusenko, John W. MacQuarrie

We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and…

math.GR2021

Blocks of profinite groups with cyclic defect group

Ricardo J. Franquiz Flores, John W. MacQuarrie

We demonstrate that the blocks of a profinite group whose defect groups are cyclic have a Brauer tree algebra structure analogous to the case of finite groups. We show further that…