Abstract Let be a field of formal Laurent series with coefficients in finite characteristic $p$?> , G_{ the maximal quotient Galois group period and nilpotency class $ $\{\mathscr G_{ filtration by ramification subgroups upper numbering. G_{ identification nilpotent Artin-Schreier theory: here $G(\mathscr is obta...

The notion of a subtractive category recently introduced by the author, is a pointed categorical counterpart of the notion of a subtractive variety of universal algebras in the sense of A. Ursini (recall that a variety is subtractive if its theory contains a constant 0 and a binary term s satisfying s(x, x) = 0 and s(x, 0) = x). Let us call a pointed regular category C normal if every regular e...

Self equivalences of classifying spaces of p-local compact groups are well understood by means of the algebraic structure that gives rise to them, but explicit descriptions are lacking. In this paper we use Robinson’s construction of an amalgam G, realising a given fusion system, to produce a split epimorphism from the outer automorphism group of G to the group of homotopy classes of self homot...

One idea how to prove that a finitely presented group G is infinite is to construct suitable homomorphisms into infinite matrix groups. In [HoP 92] this is done by starting with a finite image H of G and solving linear equations to check whether the epimorphism onto H can be lifted to a representation whose image is an extension of a ZZ-lattice by H, thus exhibiting an infinite abelian section ...

In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...

Let $n,m\in \mathbb{N}$, and let $B_{n,m}(\mathbb{R}P^2)$ be the set of $(n + m)$-braids projective plane whose associated permutation lies in subgroup $S_n\times S_m$ symmetric group $S_{n+m}$. We study splitting problem following generalisation Fadell-Neuwirth short exact sequence: $$1\rightarrow B_m(\mathbb{R}P^2 \setminus \{x_1,\dots,x_n\})\rightarrow B_{n,m}(\mathbb{R}P^2)\xrightarrow{\bar...

The notion of a subtractive category, recently introduced by the author, is a “categorical version” of the notion of a (pointed) subtractive variety of universal algebras, due to A.Ursini. We show that a subtractive variety C, whose theory contains a unique constant, is abelian (i.e. C is the variety of modules over a fixed ring), if and only if the dual category Cop of C, is subtractive. More ...

This is the first of two articles studying the structure of left adequate and, more generally, of left Ehresmann monoids. Motivated by a careful analysis of normal forms, we introduce here a concept of proper for a left adequate monoid M . In fact, our notion is that of T -proper, where T is a submonoid of M . We show that any left adequate monoid M has an X∗proper cover for some set X , that i...

This article is the second of two presenting a new approach to left adequate monoids. In the first, we introduced the notion of being T -proper, where T is a submonoid of a left adequate monoid M . We showed that the free left adequate monoid on a set X is X∗-proper. Further, any left adequate monoid M has an X∗-proper cover for some set X , that is, there is an X∗proper left adequate monoid M̂ ...

Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...