We show that the minimal base size b (G) of a finite primitive permutation group G of degree
n is at most 2 (log⁡| G|/log⁡ n)+ 24. This bound is asymptotically best possible since there …

Abstract Let G≤ GL (V) be a group with a unique subnormal quasisimple subgroup E (G)
that acts absolutely irreducibly on V. A base for G acting on V is a set of vectors with trivial …

Let V be a finite-dimensional vector space over a finite field, and suppose G≤ Γ L (V) is a
group with a unique subnormal quasisimple subgroup E (G) that is absolutely irreducible on …

We prove character ratio bounds for finite exceptional groups of Lie type. These take the
form for all nontrivial irreducible characters and nonidentity elements, where is an absolute …

For $ G $ an algebraic group of type $ A_l $ over an algebraically closed field of
characteristic $ p $, we determine all irreducible rational representations of $ G $ in defining …

• In chemistry, group theory provides a method for determining whether two molecules are
isomeric.• In quantum physics, groups and their representations are used to describe the …