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Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the Finite Simple Group Classification
group representations normal varieties Galois strati cation
2011/2/25
H. Davenport's Problem asks: What can we expect of two polynomials,over Z, with the same ranges on almost all residue class elds?This stood out among many separated variable problems posed by Davenpo...
The biHecke monoid of a finite Coxeter group and its representations
Coxeter groups Hecke algebras representation theory blocks of permutation matrices
2011/1/19
For any finite Coxeter group W, we introduce two new objects:its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matr...
A Non-Linear Locally Finite Simple Group with a p-Group as Centralizer
Non-Linear Locally Finite Simple Group p-Group
2010/2/26
We show that there exists a non-linear, locally finite, simple group such that the centralizer of every non-trivial element is (locally solvable)-by-finite.