Rationality problem for transitive subgroups of S8

Noether’s Problem and Q-generic Polynomials for the Normalizer of the 8-cycle in S8 and Its Subgroups

We study Noether’s problem for various subgroups H of the normalizer of a group C8 generated by an 8-cycle in S8, the symmetric group of degree 8, in three aspects according to the way they act on rational function fields, i.e., Q(X0, . . . , X7), Q(x1, . . . , x4), and Q(x, y). We prove that it has affirmative answers for those H containing C8 properly and derive a Q-generic polynomial with fo...

Noether's problem and ℚ-generic polynomials for the normalizer of the 8-cycle in S8 and its subgroups

We study Noether’s problem for various subgroups H of the normalizer of a group C8 generated by an 8-cycle in S8, the symmetric group of degree 8, in three aspects according to the way they act on rational function fields, i.e., Q(X0, . . . , X7), Q(x1, . . . , x4), and Q(x, y). We prove that it has affirmative answers for those H containing C8 properly and derive a Q-generic polynomial with fo...

Regular Subgroups of a Transitive Substitution Group.

Transitive Permutation Groups without Semiregular Subgroups

A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups a...

Block-transitive designs and maximal subgroups of finite symmetric groups

of finite symmetric groups.