arXiv subjects
Publications and source records attributed to David Gluck.
Let G be a primitive permutation group on a finite set Omega. Let p^2 divide |G|, for a prime p. We show that when G is solvable, there exists a subset of Omega whose stabilizer S has the property that 1<|S|_p<|G|_p. We offer a counting argument which should be helpful when G is not solvable.
Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.
Let n be an odd integer greater than 1. We slice a circular pizza into 2n slices, making cuts from a non-central interior point of the circle. We estimate the difference between between the total area of the even numbered slices and the total area of the odd numbered slices.