10 papers
Norms in Central Simple Algebras
Daniel Goldstein, Murray Schacher
Let A be a central simple algebra central over a number field K whose ring of integers is R. An outlier is an element r of R so that: r is a reduced norm of an element of A, but no…
A lower bound for the dimension of a highest weight module
Daniel Goldstein, Robert Guralnick, Richard Stong
For each integer and each complex simple Lie algebra , we determine the least dimension of an irreducible highest weight representation of whose…
On the Steinhaus tiling problem in three dimensions
Daniel Goldstein, R. Daniel Mauldin
H. Steinhaus asked in the 1950's whether there exists a set in the plane R^2 meeting every isometric copy of Z^2 in precisely one point. Such a "Steinhaus set" was constructed by J…
Cosets of Sylow p-subgroups and a Question of Richard Taylor
Daniel Goldstein, Robert M. Guralnick
We prove that for any prime p there exist infinitely many finite simple groups G with a coset xP of a Sylow p-subgroup P of G such that every element of xP has order divisible by p…
Certain subgroups of Weyl groups are split
Daniel Goldstein, Robert Guralnick
Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbe…
Nonisomorphic curves that become isomorphic over extensions of coprime degrees
Daniel Goldstein, Robert M. Guralnick, Everett W. Howe +1
We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one anot…