We classify all pairs (G, V ) with G a closed subgroup in a classical group G with natural module V over C, such that G and G have the same composition factors on V âŠ—k for a fixed k âˆˆ {2, 3, 4}. Inâ€¦ (More)

Introduction: When G is a finite group, we may endow GÃ—G with the structure of a probability space by assigning the uniform distribution. As was pointed out by W.H. Gustafson [10], the probabilityâ€¦ (More)

We classify the small irreducible representations of Sp2n(q) with q even in odd characteristic. This improves even the known results for complex representations. The smallest representation for thisâ€¦ (More)

There is a constant C0 such that all nonabelian finite simple groups of rank n over Fq , with the possible exception of the Ree groups G2(3), have presentations with at most C0 generators andâ€¦ (More)

Each group G of n Ã— n permutation matrices has a corresponding permutation polytope, P (G) := conv(G) âŠ‚ R. We relate the structure of P (G) to the transitivity of G. In particular, we show that if Gâ€¦ (More)

If f is a nonzero complex-valued function defined on a finite abelian group A and fÌ‚ is its Fourier transform, then | supp(f)|| supp(fÌ‚)| â‰¥ |A|, where supp(f) and supp(fÌ‚) are the supports of f andâ€¦ (More)

Let G be any of the groups (P )GL(n, q), (P )SL(n, q). Define a (simple) graph Î“ = Î“(G) on the set of elements of G by connecting two vertices by an edge if and only if they generate G. We prove thatâ€¦ (More)

In 1923 Schur considered the following problem. Let f âˆˆ Z[X] be a polynomial that induces a bijection on the residue fields Z/pZ for infinitely many primes p. His conjecture, that such polynomialsâ€¦ (More)