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Architectures depict design principles: paradigms that can be understood by all, allow thinking on a higher plane and avoiding low-level mistakes. They provide means for ensuring correctness by construction by enforcing global properties characterizing the ...
Architectures depict design principles: paradigms that can be understood by all, allow thinking on a higher plane and avoiding low-level mistakes. They provide means for ensuring correctness by construction by enforcing global properties characterizing the ...
Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independen ...
In this short note, we investigate some consequences of the vanishing of simple biset functors. As a corollary, if there is no non-trivial vanishing of simple biset functors (e.g., if the group G is commutative), then we show that kB(G,G) is a quasi-heredi ...
Thévenaz [6] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group G is equal to the rank of the matrix of the numbers of double cosets in G. We give another proof of this fact and present a fusion syste ...
Motivated by the Benjamini-Schramm non-unicity of percolation conjecture we study the following question. For a given finitely generated nonamenable group Gamma, does there exist a generating set S such that the Cayley graph (Gamma, S), without loops and m ...
For G a simple algebraic group over an algebraically closed field of characteristic 0, we determine the irreducible representations ρ:G→I(V), where I(V) denotes one of the classical groups SL(V), Sp(V), SO(V), such that ρ sends some distinguished unipotent ...
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic not equal 2 to contain a maximal torus of a given type. ...
The notion of active sum provides an analogue for groups of what the direct sum is for abelian groups. One natural question then is which groups are the active sum of a family of cyclic subgroups. Many groups have been found to give a positive answer to th ...
We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied by Reiter in 19 ...
