On Certain Maximal Subgroups of Symmetric or Alternating Groups.
On Prime Ideals in Representation Rings.
On some Jordan-Hölder-Dedekind type theorems in lattices.
On Subgroups Generated by a Root Triple.
On the compositum of all degree extensions of a number field
We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of Bombieri and...
On the dimension of finite permutation group actions.
On the Livingstone-Wagner theorem.
On the order of transitive permutation groups with cyclic point-stabilizer
If is a transitive permutation group of degree with cyclic point-stabilizer, then the order of is at most .
On the Sylow Subgroups of a Doubly Transitive Permuatation Group.