In this note, I propose the following conjecture : a finite group G is nilpotent if and only if its largest quotient B-group β(G) is nilpotent. I give a proof of this conjecture under the additional assumption that G be solvable. I also show that this conjecture is equivalent to the following : the kernel of restrictions to nilpotent subgroups is a biset-subfunctor of the Burnside functor. AMS ...

Let G be a finite group, p prime, and (K,O,F) p-modular system. We prove that the trivial source ring of OG is isomorphic to coherent G-stable tuples (χP), where χP virtual character K[NG(P)/P], P runs through all p-subgroups G, coherence condition equality certain values. use this result describe group orthogonal units as product unit Burnside fusion system with (φP) homomorphisms NG(P)/P→F×. ...

We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max;+)-algebra (that is, the semiring (R[ f 1g;max;+)), and also for semigroups of (max;+)-linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed. Key-words: Semigroups, Burnside Prob...

I f G induces a primitive permutation group on the set X of points (l-spaces) of the underlying vector space V, then well-known results of Burnside [I, p. 3411 and Schur [6] imply that G acts on X 2-transitively or as a regular or Frobenius group of prime degree; the theorem then follows from [2; 51. We must thus take a nontrivial block of imprimitivity d for G on X, and analyze the action of G...

Contact Information Developing an online database of descriptions of ectomycorrhizae 1. Research Scientist, Canadian Forest Service, Natural Resources Canada, Pacific Forestry Centre, 506 Burnside Road West, Victoria, BC, V8Z 1M5. Email: [email protected] 2. Biologist, Canadian Forest Service, Natural Resources Canada, Pacific Forestry Centre, 506 Burnside Road West, Victoria, BC, V8Z 1...

We prove a broad generalization of theorem W. Burnside about the existence real characters finite groups to permutation characters. If G is group, under necessary hypothesis O 2 ′ ( ) = , we can also give some control on parity multiplicities constituents (a result that needs Classification Finite Simple Groups). Along way, new characterization 2-closed using odd-order elements group. All this ...

Let G be a compact Lie group and A(G) its Burnside Ring. For a compact smooth n-dimensional G-manifold X equipped with a generic Ginvariant vector field v, we prove an equivariant analog of the Morse formula Ind(v) = n