6 citations · 17 across the 17 of their papers we have counts for
6 papers · 2 filters
Comparing the order and the minimal number of generators of a finite irreducible linear group
Derek Holt, Gareth Tracey
We prove that for irreducible subgroups of GL, and estimate the associated constants. The result is motivated by attempts to bound the co…
Totally -closed finite groups with trivial Fitting subgroup
Majid Arezoomand, Mohammad A. Iranmanesh, Cheryl E. Praeger +1
A group is said to be totally -closed if in each of its faithful permutation representations, say on a set , is the largest subgroup of which leaves…
On the proportion of -elements in a finite group, and a modular Jordan type theorem
Gareth Tracey
In 1878, Jordan proved that if a finite group has a faithful representation of dimension over , then has a normal abelian subgroup with index bounded above…
The transitive groups of degree 48 and some applications
Derek Holt, Gordon Royle, Gareth Tracey
The primary purpose of this paper is to report on the successful enumeration in Magma of representatives of the conjugacy classes of transitive subgroups of the sym…
Sharp upper bounds on the minimal number of elements required to generate a transitive permutation group
Gareth Tracey
The purpose of this paper is to prove that if is a transitive permutation group of degree , then can be generated by elements, w…
Some simplifications in the proof of the Sims conjecture
László Pyber, Gareth Tracey
We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.