Cheryl E. Praeger

activity

20092026

most citedPartial linear spaces with a rank 3 affine primitive group of automorphisms

7 citations · 19 across the 30 of their papers we have counts for

collaborators

34 papers

math.CO2026

A new flag-transitive linear space

Seyed Hassan Alavi, Ashraf Daneshkhah, Martin W. Liebeck +1

We construct a new flag-transitive $2$ - $(496, 4, 1)$ design with automorphism group $PΓL_{2} (32)$ . This corrects an omission in the classification of the finite flag-transitiv…

math.CO2026

Recursive constructions for block-transitive, poset-imprimitive two-designs

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We give two general constructions for $2$ -designs, that can be used recursively, and interchangeably, to produce new infinite families of $2$ -designs admitting block-transitive gro…

math.GR2026

The probability that two elements with large $1$ -eigenspaces generate a classical group

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger

With high probability, among $O (lo g n)$ independent randomly selected elements from a finite $n$ -dimensional classical group, some pair of elements power to a $2$ -element generati…

math.CO2025

Quasiprimitive and bi-quasiprimitive highly-arc-transitive digraphs and finite simple groups

Lei Chen, Cheryl Praeger

We extend the notion of an $H$ -normal quotient digraph of an $H$ -vertex-transitive digraph to that of an $H$ -subnormal quotient digraph. Using these concepts, together with biparti…

math.GR2025

Block-transitive designs with a poset of imprimitive partitions

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We study block designs which admit an automorphism group that is transitive on blocks and points, and leaves invariant every partition in a given finite poset of partitions of the…

math.GR2025

Enhanced power graphs of finite groups with cograph structure

Daniela Bubboloni, Francesco Fumagalli, Cheryl E. Praeger

The enhanced power graph, $E (G)$ , of a group $G$ has vertex set $G$ and two elements are adjacent if they generate a cyclic subgroup. In the case of finite groups, we ide…

math.GR2025

Finite permutation groups with quasi-semiregular elements

Michael Giudici, Luke Morgan, Cheryl E. Praeger

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in t…

math.GR2025

Proper partial linear spaces affording imprimitive rank 3 automorphism groups

Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger

A partial linear space is a point--line incidence structure such that each line is incident with at least two points and each pair of points is incident with at most one line. It i…

math.GR2024

Prime power coverings of groups

Michael Giudici, Luke Morgan, Cheryl E. Praeger

For a finite group $A$ with normal subgroup $G$ , a subgroup $U$ of $G$ is an $A$ -prime-power-covering subgroup if $U$ meets every $A$ -conjugacy-class of elements of $G$ of prime po…

math.GR2024★ 1 cited

Finite simple groups have many classes of $p$ -elements

Michael Giudici, Luke Morgan, Cheryl E. Praeger

For an element $x$ of a finite group $T$ , the $Aut (T)$ -class of $x$ is the set ${x^{σ} ∣ σ \in Aut (T)}$ . We prove that the order $∣ T ∣$ of a finite nonabelian si…

math.RT2024

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger +1

This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $G L_{d} (F_{q})$ for which some element $g \in G$ of prime order $…

math.CO2024

Vertex-primitive s-arc-transitive digraphs of symplectic groups

Lei Chen, Michael Giudici, Cheryl E. Praeger

A digraph is $s$ -arc-transitive if its automorphism group is transitive on directed paths with $s$ edges, that is, on $s$ -arcs. Although infinite families of finite $s$ -arc transit…

math.CO2024★ 2 cited

Basic Tetravalent Oriented Graphs of Independent-Cycle Type

Nemanja Poznanovic, Cheryl E. Praeger

The family $OG (4)$ consisting of graph-group pairs $(Γ, G)$ , where $Γ$ is a finite, connected, 4-valent graph admitting a $G$ -vertex-, and $G$ -edge-transitive, but not $G…

math.CO2024

Group actions on codes in graphs

Daniel R. Hawtin, Cheryl E. Praeger

This is a chapter in a forthcoming book on completely regular codes in distance regular graphs. The chapter provides an overview, and some original results, on codes in distance re…

math.GR2024

Maps, simple groups, and arc-transitive graphs

Martin W. Liebeck, Cheryl E. Praeger

We determine all factorisations $X = A B$ , where $X$ is a finite almost simple group and $A, B$ are core-free subgroups such that $A \cap B$ is cyclic or dihedral. As a main application…

math.GR2024

Constructive Recognition of Special Linear Groups

Max Horn, Alice Niemeyer, Cheryl Praeger +1

We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d \times d$ matrices…

math.CO2024

Higher-dimensional grid-imprimitive block-transitive designs

Seyed Hassan Alavi, Carmen Amarra, Ashraf Daneshkhah +2

It was shown in 1989 by Delandtsheer and Doyen that, for a $2$ -design with $v$ points and block size $k$ , a block-transitive group of automorphisms can be point-imprimitive (that i…

math.CO2024

Chain-imprimitive, flag-transitive 2-designs

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

We consider $2$ -designs which admit a group of automorphisms that is flag-transitive and leaves invariant a chain of nontrivial point-partitions. We build on our recent work on $2$ …

math.CO2024

Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients

Nemanja Poznanovic, Cheryl E. Praeger

Let $OG (4)$ denote the family of all graph-group pairs $(Γ, G)$ where $Γ$ is finite, 4-valent, connected, and $G$ -oriented ( $G$ -half-arc-transitive). A subfamily of $\mat…

math.GR2023

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger

Let $V := (F_{q})^{d}$ be a $d$ -dimensional vector space over the field $F_{q}$ of order $q$ . Fix positive integers $e_{1}, e_{2}$ satisfying $e_{1} + e_{2} = d$ . Motivated by analysi…

math.CO2023

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

A \emph{mixed dihedral group} is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\con…

math.CO2023

Block-transitive 2-designs with a chain of imprimitive partitions

Carmen Amarra, Alice Devillers, Cheryl E. Praeger

More than $30$ years ago, Delandtsheer and Doyen showed that the automorphism group of a block-transitive $2$ -design, with blocks of size $k$ , could leave invariant a nontrivial po…

math.CO2023

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

Daniel R. Hawtin, Jin-Xin Zhou, Cheryl E. Praeger

A mixed dihedral group is a group $H$ with two disjoint subgroups $X$ and $Y$ , each elementary abelian of order $2^{n}$ , such that $H$ is generated by $X \cup Y$ , and $H/H'\cong X\tim…

math.GR2022★ 5 cited

Rank three innately transitive permutation groups and related $2$ -transitive groups

Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analo…

A new flag-transitive linear space

Recursive constructions for block-transitive, poset-imprimitive two-designs

The probability that two elements with large 1-eigenspaces generate a classical group

Quasiprimitive and bi-quasiprimitive highly-arc-transitive digraphs and finite simple groups

Block-transitive designs with a poset of imprimitive partitions

Enhanced power graphs of finite groups with cograph structure

Finite permutation groups with quasi-semiregular elements

Proper partial linear spaces affording imprimitive rank 3 automorphism groups

Prime power coverings of groups

Finite simple groups have many classes of p-elements

Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime

Vertex-primitive s-arc-transitive digraphs of symplectic groups

Basic Tetravalent Oriented Graphs of Independent-Cycle Type

Group actions on codes in graphs

Maps, simple groups, and arc-transitive graphs

Constructive Recognition of Special Linear Groups

Higher-dimensional grid-imprimitive block-transitive designs

Chain-imprimitive, flag-transitive 2-designs

Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients

Bipartite q-Kneser graphs and two-generated irreducible linear groups

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite 2-arc-transitive graph which is not a Cayley graph

Block-transitive 2-designs with a chain of imprimitive partitions

A family of 2-groups and an associated family of semisymmetric, locally 2-arc-transitive graphs

Rank three innately transitive permutation groups and related 2-transitive groups

The probability that two elements with large $1$ -eigenspaces generate a classical group

Finite simple groups have many classes of $p$ -elements

Bipartite $q$ -Kneser graphs and two-generated irreducible linear groups

Using mixed dihedral groups to construct normal Cayley graphs, and a new bipartite $2$ -arc-transitive graph which is not a Cayley graph

A family of $2$ -groups and an associated family of semisymmetric, locally $2$ -arc-transitive graphs

Rank three innately transitive permutation groups and related $2$ -transitive groups