Let S be a nite nonabelian simple group, and let H be a subgroup of S. In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and suucient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of nite nonabelian simple groups. An epimo...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

a group is called morphic if for each normal endomorphism α in end(g),there exists β such that ker(α)= gβ and gα= ker(β). in this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= gβ and gα = ker(γ). we call g quasi-morphic, if this happens for any normal endomorphism α in end(g). we get the following results: g is quasi-morphic if and only if, for any ...

Given a directed graph G = (V, E) an independent set A ⊂ V is called quasi-kernel (quasi-sink) iff for each point v there is a path of length at most 2 from some point of A to v (from v to some point of A). Every finite directed graph has a quasikernel. The plain generalization for infinite graphs fails, even for tournaments. We investigate the following conjecture here: for any digraph G = (V,...

We show that every Π1-elementary epimorphism between models of ZF is an isomorphism. On the other hand, nonisomorphic Σ1-elementary epimorphisms between models of ZF can be constructed, as can fully elementary epimorphisms between models of ZFC−. Elementary epimorphisms were introduced by Philipp Rothmaler in [Rot05]. A surjective homomorphism f : M → N between two model-theoretic structures is...

We show that there exist infinitely many examples of pairs of knots, K1 and K2, that have no epimorphism π1(S 3 \K1)→ π1(S \K2) preserving peripheral structure although their A-polynomials have the factorization AK2(L,M) | AK1(L,M). Our construction accounts for most of the known factorizations of this form for knots with 10 or fewer crossings. In particular, we conclude that while an epimorphi...

The Coxeter simplex with symbol is a compact hyperbolic 4-simplex and the related Coxeter group Γ is a discrete subgroup of Isom(H 4). The Coxeter simplex with symbol is a spherical 3-simplex, and the related Coxeter group G is the group of symmetries of the regular 120-cell. Using the geometry of the regular 120-cell, Davis [3] constructed an epimorphism Γ → G whose kernel K was torsion-free, ...