Cheryl E. Praeger

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20242026

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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.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

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.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

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…

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

Block-transitive designs with a poset of imprimitive partitions

Enhanced power graphs of finite groups with cograph structure

Proper partial linear spaces affording imprimitive rank 3 automorphism groups

Finite permutation groups with quasi-semiregular elements

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

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

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