Abstract Let D=(P, B) be a symmetric 2-(v, k, λ) design admitting a flag-transitive, point-
imprimitive automorphism group G that leaves invariant a non-trivial partition Σ of P. Praeger …

A kk‐tuple (H 1,…, H k) (H_1,...,H_k) of core‐free subgroups of a finite group GG is said to be
regular if GG has a regular orbit on the Cartesian product G/H 1×⋯× G/H k G/H_1*⋯*G/H_k …

In this paper, we determine the finite groups with a Sylow r-subgroup contained in a unique
maximal subgroup. The proof involves a reduction to almost simple groups, and our main …

Given a permutation group 𝐺, the derangement graph of 𝐺 is the Cayley graph with
connection set the derangements of 𝐺. The group 𝐺 is said to be innately transitive if 𝐺 has a …

Let M be the Monster group, which is the largest sporadic finite simple group, and has first
been constructed in 1982 by Griess. In 1985 Conway has constructed a 196884 …

Let $ G\leqslant {\rm Sym}(\Omega) $ be a finite transitive permutation group and recall that
an element in $ G $ is a derangement if it has no fixed points on $\Omega $. Let $\Delta (G) …

Let G be a group such that is finite and simple. The non-commuting, non-generating graph of
G has vertex set, with edges corresponding to pairs of elements that do not commute and do …

Resolvent degree is an invariant measuring the complexity of algebraic and geometric
phenomena, including the complexity of finite groups. To date, the resolvent degree of a …

If H is a Hall subgroup of a finite group G, it was proven in 1989 using the classification of
finite simple groups that all the irreducible complex characters of H extend to G if and only if …

“The essence of math is not to make simple things complicated, but to make complicated
things simple” 1, a principle mirrored in algorithms since they serve as the computational …