Tomasz Popiel

activity

20122023

most citedAn exotic presentation of Q_28

10 citations · 39 across the 18 of their papers we have counts for

collaborators

20 papers

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The classification of the maximal subgroups of the Monster $M$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $M$ …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★ 9 cited

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.GR2021

$M$ , $B$ and $Co_{1}$ are recognisable by their prime graphs

Melissa Lee, Tomasz Popiel

The prime graph, or Gruenberg--Kegel graph, of a finite group $G$ is the graph $Γ (G)$ whose vertices are the prime divisors of $∣ G ∣$ , and whose edges are the pairs ${p, q}$ for wh…

math.CO2021

Solids in the space of the Veronese surface in even characteristic

Nour Alnajjarine, Michel Lavrauw, Tomasz Popiel

We classify the orbits of solids in the projective space $PG (5, q)$ , $q$ even, under the setwise stabiliser $K ≅ PGL (3, q)$ of the Veronese surface. For each orbit,…

math.CO2020

Combinatorial invariants for nets of conics in $PG (2, q)$

Michel Lavrauw, Tomasz Popiel, John Sheekey

The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over $C$ …

math.CO2020★ 5 cited

Nets of conics of rank one in PG(2,q), q odd

Michel Lavrauw, Tomasz Popiel, John Sheekey

We classify nets of conics in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof…

math.AT2019★ 10 cited

An exotic presentation of Q_28

Wajid Mannan, Tomasz Popiel

We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has non-standard second homotopy…

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.CO2017★ 2 cited

The symmetric representation of lines in $PG (F^{3} \otimes F^{3})$

Michel Lavrauw, Tomasz Popiel

Let $F$ be a finite field, an algebraically closed field, or the field of real numbers. Consider the vector space $V = F^{3} \otimes F^{3}$ of $3 \times 3$ mat…

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…

math.GR2015

Finding involutions with small support

Alice C. Niemeyer, Tomasz Popiel

We show that the proportion of permutations $g$ in $S_{n}$ or $A_{n}$ such that $g$ has even order and $g^{∣ g ∣/2}$ is an involution with support of cardinality at most $\lceil n^\varep…

math.GR2015

Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type

Luke Morgan, Tomasz Popiel

Let $G$ be a collineation group of a thick finite generalised hexagon or generalised octagon $Γ$ . If $G$ acts primitively on the points of $Γ$ , then a recent result of Bamberg et a…

math.GR2015

Point-primitive, line-transitive generalised quadrangles of holomorph type

John Bamberg, Tomasz Popiel, Cheryl E. Praeger

Let $G$ be a group of collineations of a finite thick generalised quadrangle $Γ$ . Suppose that $G$ acts primitively on the point set $P$ of $Γ$ , and transitively on the l…

math.CO2014★ 2 cited

Point-primitive generalised hexagons and octagons

John Bamberg, S. P. Glasby, Tomasz Popiel +2

In 2008, Schneider and Van Maldeghem proved that if a group acts flag-transitively, point-primitively, and line-primitively on a generalised hexagon or generalised octagon, then it…

math.CO2014

Generalised quadrangles and transitive pseudo-hyperovals

John Bamberg, Stephen P. Glasby, Tomasz Popiel +1

A pseudo-hyperoval of a projective space $\PG(3n-1,q)$, $q$ even, is a set of $q^{n} + 2$ subspaces of dimension $n - 1$ such that any three span the whole space. We prove that a pseudo-…

math.GR2014★ 1 cited

Nilpotent-independent sets and estimation in matrix algebras

Brian P. Corr, Tomasz Popiel, Cheryl E. Praeger

Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selectio…

cs.DS2013

Showcasing straight-line programs with memory via matrix Bruhat decomposition

Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger +1

We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of f…

math.GR2012★ 9 cited

Abundant p-singular elements in finite classical groups

Alice C. Niemeyer, Tomasz Popiel, Cheryl E. Praeger

In 1995, Isaacs, Kantor and Spaltenstein proved that for a finite simple classical group G defined over a field with q elements, and for a prime divisor p of |G| distinct from the…

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

M, B and Co1​ are recognisable by their prime graphs

Solids in the space of the Veronese surface in even characteristic

Combinatorial invariants for nets of conics in PG(2,q)

Nets of conics of rank one in PG(2,q), q odd

An exotic presentation of Q_28

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

The symmetric representation of lines in PG(F3⊗F3)

Simple groups, product actions, and generalised quadrangles

Finding involutions with small support

Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type

Point-primitive, line-transitive generalised quadrangles of holomorph type

Point-primitive generalised hexagons and octagons

Generalised quadrangles and transitive pseudo-hyperovals

Nilpotent-independent sets and estimation in matrix algebras

Showcasing straight-line programs with memory via matrix Bruhat decomposition

Abundant p-singular elements in finite classical groups

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

$M$ , $B$ and $Co_{1}$ are recognisable by their prime graphs

Combinatorial invariants for nets of conics in $PG (2, q)$

The symmetric representation of lines in $PG (F^{3} \otimes F^{3})$