Let G be a finite group, p a prime, and S a Sylow p-subgroup of G. Subsets of S are said to be fused in G if they are conjugate under some element of G. The term “fusion” seems to have been introduced by Brauer in the fifties, but the general notion has been of interest for over a century. For example in his text The Theory of Groups of Finite Order [Bu] (first published in 1897), Burnside prov...

Let G be a (not necessarily finite) group and p a finite dimensional faithful irreducible representation of G over an arbitrary field; write ~p for p viewed as a projective representation. Suppose that p is not induced (from any proper subgroup) and that ~p~ is not a tensor product (of projective representations of dimension greater than 1 ). Let AT be a noncentral subgroup which centralizes al...

group GC defined over Q whose connected component G 0 Q has no rational character. It is also necessary to suppose that the centralizer of a maximal Q split torus of G0C meets every component of GC. The reduction theory of Borel applies, with trivial modifications, to G; it will be convenient to assume that Γ has a fundamental set with only one cusp. Fix a minimal parabolic subgroup P 0 C defin...

Given a unital algebra A of linear transformations on finite-dimensional complex vector space V, in this paper we study the set Col(A) consisting those invertible S V which map every subspace M∈Lat(A) to SM∈Lat(A). We show that is normalizer group reflexive cover A. For (A) generated by transformation A, give complete description Col(A). By using primary decomposition first reduce problem chara...

The fusion orbit category F‾C(G) of a discrete group G over collection C is the whose objects are subgroups H in C, and morphisms H→K given by G-maps G/H→G/K modulo action centralizer CG(H). We show that higher limits can be computed using hypercohomology spectral sequences coming from Dwyer G-spaces for normalizer decompositions G. If realizing saturated system F, then these give two converge ...

Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred homomorphism to the normalizer of the maximal torus; i.e. that “norm...

the present note arises from the author's talk at the conference ``ischia group theory 2014''. for subgroups $fle n$ of a group $g$ denote by $lat(f,n)$ the set of all subgroups of $n$, containing $f$. let $d$ be a subgroup of $g$. in this note we study the lattice $ll=lat(d,g)$ and the lattice $ll'$ of subgroups of $g$, normalized by $d$. we say that $ll$ satisfies sandwich classification theo...

A fundamental problem for network intrusion detection systems is the ability of a skilled attacker to evade detection by exploiting ambiguities in the traffic stream as seen by the monitor. We discuss the viability of addressing this problem by introducing a new network forwarding element called a traffic normalizer. The normalizer sits directly in the path of traffic into a site and patches up...

We present an Agda formalization of a normalization proof for simply-typed lambda terms. The normalizer consists of two coinductively defined functions in the delay monad: One is a standard evaluator of lambda terms to closures, the other a type-directed reifier from values to η-long β-normal forms. Their composition, normalization-by-evaluation, is shown to be a total function a posteriori, us...