1. Abstract characterization of Dn The group Dn has two generators r and s with orders n and 2 such that srs−1 = r−1. We will show any group with a pair of generators like r and s (except for their order) admits a homomorphism onto it from Dn, and is isomorphic to Dn if it has the same size as Dn. Theorem 1.1. Let G be generated by elements a and b where an = 1 for some n ≥ 3, b2 = 1, and bab−1...

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

ρ(e)(x) = e · x A1 = x = 1X(x) for all g, h ∈ G and x ∈ X. Thus ρ(gh) = ρ(g) ◦ ρ(h), ρ(e) = 1X and ρ is hence a homomorphism of monoids G → M(X). Then we note 1X = ρ(e) = ρ(gg ) = ρ(g) ◦ ρ(g) and similarly 1X = ρ(g) ◦ ρ(g) and so the ρ(g) are bijections G → G for all g ∈ G. Thus ρ is a homomorphism G → Σ(X). Given a homomorphism λ : G → Σ(X), in order for it to be the action homomorphism of an ...

We study the image of a transfer homomorphism in the stable homotopy groups of spheres. Actually, we show that an element of order 8 in the 18 dimensional stable stem is in the image of a double transfer homomorphism, which reproves a result due to P J Eccles that the element is represented by a framed hypersurface. Also, we determine the image of the transfer homomorphism in the 16 dimensional...

In this paper we propose right-angled Artin groups as platform for a secret sharing scheme based on the efficiency (linear time) of the word problem. We define two new problems: subgroup isomorphism problem for Artin subgroups and group homomorphism problem in right-angled Artin groups. We show that the group homomorphism and graph homomorphism problems are equivalent, and the later is known to...

Let G and G' be multiplicative systems. A half-homomorphism of G into G' will mean a mapping a—>a' of G into C such that for all a, bEG, (ab)'=a'V or b'a'. An anti-homomorphism is a mapping such that always (ab)' = b'a'. The terms half-isomorphism, etc., are defined similarly. It will be shown that any half-homomorphism of a group G into a group G' is either a homomorphism or an anti-homomorphi...

1. Let G be an algebraic linear group over a field F. If G acts by linear automorphisms on some vector space M over F we say that M is a rational G-module if it is the sum of finite-dimensional G-stable subspaces V such that the representation of G on each F is a rational representation of G. The rational G-module M is said to be rationally injective if, whenever U is a rational G-module and 0 ...

Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinato...

It is not difficult to see that every group homomorphism from Z to R extends to a homomorphism from R to R. (Essentially, this is the fact that a linear transformation can be defined to have any desired action on a basis.) We will see other examples of discrete subgroups Γ of connected groups G, such that the homomorphisms defined on Γ can (“almost”) be extended to homomorphisms defined on all ...