The paper [FGS] uses the classification of finite simple groups and covering theory in positive characteristic to solve Carlitz’s conjecture (1966). We consider only separable polynomials; their derivative is nonzero. Then, f ∈ Fq [x] is exceptional if it acts as a permutation map on infinitely many finite extensions of the finite field Fq , q = pa for some prime p. Carlitz’s conjecture says f ...

Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.

The study of branched covers of the Riemann sphere has connections to many fields. We recall the classical relationship between branched covers and group theory via the Riemann existence theorem, which then leads to represention-theoretic formulas for Hurwitz numbers, counting the number of branched covers of prescribed types. We also review the Hurwitz spaces parametrizing branched covers as w...

Let A L $A_L$ be the right-angled Artin group associated with a finite flag complex $L$ . We show that amenable category of equals virtual cohomological dimension Coxeter W $W_L$ In particular, groups satisfy question Capovilla–Löh–Moraschini proposing an inequality between and Farber's topological complexity.

We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a certain hypergeometric differential equation. This generalizes the result of Deligne and Rapoport on the reduction of the modular curve X (p).

We describe a procedure for constructing morphisms in additive categories, combining Auslander’s concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective covers, and we interprete these constructions in terms of adjoint functors.

is a monomorphism for all collections of right R-modules {Ni : i ∈ I} . Restricting the Ni to certain classes of modules one obtains various relativized concepts. For instance, Goodearl investigated this notion relativized to flat modules. The present study provides a uniform background for such relativizations and thus covers and generalizes, among others, a number of known results about such ...

Generalising the notion of Galois corings, Galois comodules were introduced as comodules P over an A-coring C for which PA is finitely generated and projective and the evaluation map μC : Hom (P, C) ⊗S P → C is an isomorphism (of corings) where S = End(P ). It was observed that for such comodules the functors HomA(P,−)⊗S P and −⊗A C from the category of right A-modules to the category of right ...