A theorem on groups
A theorem on normal semigroups
A theorem on restricted group representations.
A Theorem on the Restriction of Group Characters, and Its Application to the Character Theory of SL (n, q).
A theory of transformation monoids: combinatorics and representation theory.
A third look at weight diagrams
A tilde geometry for .
A topological view of ordered groups
In this expository article we use topological ideas, notably compactness, to establish certain basic properties of orderable groups. Many of the properties we shall discuss are well-known, but I believe some of the proofs are new. These will be used, in turn, to prove some orderability results, including the left-orderability of the group of PL homeomorphisms of a surface with boundary, which are fixed on at least one boundary component.
A Transfer Theorem for Small Primes.
A transvection decomposition in GL(n,2)
An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.
A tree as a finite nonempty set with a binary operation
A (finite) acyclic connected graph is called a tree. Let be a finite nonempty set, and let be the set of all trees with the property that is the vertex set of . We will find a one-to-one correspondence between and the set of all binary operations on which satisfy a certain set of three axioms (stated in this note).
A tropical view on Bruhat-Tits buildings and their compactifications
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...
A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux.
A unification of Knizhnik-Zamalodchikov and Dunkl operators via affine Hecke algebras.
A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups.
A unified treatment of the theories of matroids with coefficients and of -matroids with coefficients.
A uniform chain whose inverse semigroup has no chart.
A uniformly quasiconformal group not isomorphic to a Möbius group.
A unipotent group associated with certain linear groups
A useful category for mixed Abelian groups.