We determine the epimorphisms A → W from the Artin group A of type Γ onto the Coxeter group W of type Γ, in case Γ is an irreducible Coxeter graph of spherical type, and we prove that the kernel of the standard epimorphism is a characteristic subgroup of A. This generalizes an over 50 years old result of Artin. AMS Subject Classification: Primary 20F36; Secondary 20F55.

Let K be the kernel of an epimorphism G→ Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3 or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group G, then any homomorphism from K onto the symmetric group S2 (resp. Z3) lifts to a homomorphism onto S3 (resp. alternating group A4).

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact. MSC...

This paper investigates the problem of finding the possible sequences of periodic point counts for endomorphisms of solenoids. For an ergodic epimorphism of a solenoid, a closed formula is given which expresses the number of points of any given period in terms of sets of places of finitely many algebraic number fields and distinguished elements of those fields. The result extends to more genera...

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ M r(x) for all x ∈ E, where r( · ) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple C∗-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End (RZ) of the additive group RZ, taking any r ∈ R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this case RZ is called an E-group. Obvious examples of E-rings are subrings of Q. However there is a proper class of examples constructed recently, see [8]. E-rings ...

Let A be an Ä-order in a semisimple finite dimensional /(-algebra, where K is an algebraic number field, and R is the ring of algebraic integers of K. Denote by C(A) the reduced class group of the category of locally free left A-lattices. Choose A= ZC, the integral group ring of a finite group G, and let A be a maximal Z-order in QG containing A. There is an epimorphism C(A)-C(A'), given by JIÍ...

Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...

A group epimorphism Q: G+ Q preserves perfect radicals if $PG = PQ, where PC, PQ is maximal perfect in G, Q respectively. The following two questions are considered. Question 1. If P,,(B) acts trivially on H,(F; E), does the tibration F + Es B then have ~,(P)(P~,(E)) = Pm,(B)? Question 2. If f: X + Y is a map of spaces which induces an isomorphism of homology groups, is rr,(X) * rr,( Y) n,( Y)/...

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End (RZ) of the additive group RZ, taking any r ∈ R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this case RZ is called an E-group. Obvious examples of E-rings are subrings of Q. However there is a proper class of examples constructed recently, see [8]. E-rings ...