Tomasz Popiel

activity

20172023

most citedSimple groups, product actions, and generalised quadrangles

1 citations · 1 across the 6 of their papers we have counts for

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math.GR2023

Indeed, the Monster has no almost simple maximal subgroup with socle $PSL_{2} (16)$

Heiko Dietrich, Melissa Lee, Tomasz Popiel

The classification of the maximal subgroups of the Monster $M$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $M$ …

math.GR2023

Recognisability of the sporadic groups by the isomorphism types of their prime graphs

Melissa Lee, Tomasz Popiel

The prime graph of a finite group $G$ is the labelled graph $Γ (G)$ with vertices the prime divisors of $∣ G ∣$ and edges the pairs ${p, q}$ for which $G$ contains an element of orde…

math.GR2023

The maximal subgroups of the Monster

Heiko Dietrich, Melissa Lee, Tomasz Popiel

The classification of the maximal subgroups of the Monster $M$ is a long-standing problem in finite group theory. According to the literature, the classification is comple…

math.GR2021

Saxl graphs of primitive affine groups with sporadic point stabilisers

Melissa Lee, Tomasz Popiel

Let $G$ be a permutation group on a set $Ω$ . A base for $G$ is a subset of $Ω$ whose pointwise stabiliser is trivial, and the base size of $G$ is the minimal cardinality of a base.…

math.GR2017

On the second-largest Sylow subgroup of a finite simple group of Lie type

S. P. Glasby, Alice C. Niemeyer, Tomasz Popiel

Let $T$ be a finite simple group of Lie type in characteristic $p$ , and let $S$ be a Sylow subgroup of $T$ with maximal order. It is well known that $S$ is a Sylow $p$ -subgroup exc…

math.GR2017★ 1 cited

Simple groups, product actions, and generalised quadrangles

John Bamberg, Tomasz Popiel, Cheryl E. Praeger

The classification of flag-transitive generalised quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known…

Indeed, the Monster has no almost simple maximal subgroup with socle PSL2​(16)

Recognisability of the sporadic groups by the isomorphism types of their prime graphs

The maximal subgroups of the Monster

Saxl graphs of primitive affine groups with sporadic point stabilisers

On the second-largest Sylow subgroup of a finite simple group of Lie type

Simple groups, product actions, and generalised quadrangles

Indeed, the Monster has no almost simple maximal subgroup with socle $PSL_{2} (16)$