Related papers: Fusion Systems for Profinite Groups

Saturated fusion systems are categories generalizing important aspects of conjugacy of $p$-subgroups in finite groups. It was shown by Chermak that there are group-like structures called regular localities associated to saturated fusion…

Complementing and extending the Inventiones work of Benson, Grodal, Henke [Group cohomology and control of p-fusion, Invent. Math. 197 (2014), 491--507] we give criteria for a space to have cohomology (strongly) F-isomorphic in the sense of…

We prove, for certain pairs G,G of finite groups of Lie type, that the p-fusion systems for G and G' are equivalent. In other words, there is an isomorphism between a Sylow p-subgroup of G and one of G' which preserves p-fusion. This…

We prove the pro-$p$ version of the Karras, Pietrowski, Solitar, Cohen and Scott result stating that a virtually free group acts on a tree with finite vertex stabilizers. If a virtually free pro-$p$ group $G$ has finite centralizes of all…

In this paper, for any prime $p$, we propose the notion of a $p$-transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique trivial submodule to the case…

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the…

It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…

The notion of a Hopf module over a Hopf (co)quasigroup is introduced and a version of the fundamental theorem for Hopf (co)quasigroups is proven.

Let $p$ be a prime number. A saturated fusion system $\mathcal{F}$ on a finite $p$-group $S$ is said to be supersolvable if there is a series $1 = S_0 \le S_1 \le \dots \le S_m = S$ of subgroups of $S$ such that $S_i$ is strongly…

The theory of saturated fusion systems resembles in many parts the theory of finite groups. However, some concepts from finite group theory are difficult to translate to fusion systems. For example, products of normal subsystems with other…

We develop the fundamentals of Mackey functors in the setup of fusion systems including an acyclicity condition as well as a parametrization and an explicit description of simple Mackey functors. Using this machinery we extend Dwyer's…

A saturated fusion system over a finite $p$-group $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over $S$ is realized…

We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.

Let $q$ be a power of a fixed prime $p$. We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$-groups constructed from the polynomial representations of $\mathrm{SL}_2(q)$, which includes the Sylow…

Let G be a finitely generated infinite pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. Then we prove that G splits as a pro-p amalgamated product or as a pro-p HNN-extension over an…

We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP

An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.

In recent work, the second author introduced the concept of Coxeter quivers, generalizing several previous notions of a quiver representation. Finite type Coxeter quivers were classified, and their indecomposable objects were shown to be in…

We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is the \'etale…

We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of B\'arcenas--Cantarero to non-saturated fusion systems, we show that the number of indecomposable F-invariant characters…