Counting homomorphisms onto finite solvable groups

  title={Counting homomorphisms onto finite solvable groups},
  author={Daniel Matei and Alexander I. Suciu},
  journal={Journal of Algebra},

Tables from this paper

The Number of Homomorphisms From Quaternion Group into Some Finite Groups

We derive general formulae for counting the number of homomorphisms from quaternion group into each of quaternion group, dihedral group, quasi-dihedral group and modular group by using only

The Number of Group Homomorphisms from D[subscript m] into D[subscript n].

Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms

New Permutation Representations of the Braid Group

We give a new infinite family of group homomorphisms from the braid group B_k to the symmetric group S_{mk} for all k and m \geq 2. Most known permutation representations of braids are included in

On Homomorphisms from C to C

In this paper, using elementary algebra and analysis, we characterize and compute all continuous homomorphism from C to C. Also we prove that the cardinality of the set of all non-continous group

The Number of Group Homomorphisms from Dm into Dn

Summary We count the number of group homomorphisms between any two dihedral groups using elementary group theory only.

Complex Arrangements: Algebra, Geometry, Topology

A hyperplane arrangement A is a finite collection of hyperpla nes in some fixed (typically real or complex) vector space V. For simplicity, in this overview we work over the complex numbers C. There

Two paradigms for topological quantum computation

We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the

Modular Categories 3 D − TQFT Top

  • 2008



Hall invariants, homology of subgroups, and characteristic varieties

Given a finitely-generated group G, and a finite group \Gamma, Philip Hall defined \delta_\Gamma to be the number of factor groups of G that are isomorphic to \Gamma. We show how to compute the Hall

Subgroups of Finite Index in Free Groups

  • M. Hall
  • Mathematics
    Canadian Journal of Mathematics
  • 1949
This paper has as its chief aim the establishment of two formulae associated with subgroups of finite index in free groups. The first of these (Theorem 3.1) gives an expression for the total length

On a theorem of Artin

We determine the epimorphisms A --> W from the Artin group A of type Gamma onto the Coxeter group W of type Gamma, in case Gamma is an irreducible Coxeter graph of spherical type, and we prove that

Isomorphism Classes and Derived Series of Certain Almost-Free Groups

It is verified that there are different isomorphism types among the groups in the family of groups, and that the third terms in the derived series of quotients are often distinct from that of F.

Tree actions of automorphism groups

We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of one-relator groups: certain

Braids and Permutations

E. Artin described all irreducible representations of the braid group B_k to the symmetric group S(k). We strengthen some of his results and, moreover, exhibit a complete picture of homomorphisms of


The fascinating thing is that zeroth syzygies and first syzygies have an intrinsic significance in terms of the duality functor A 7→ A∗ = HomΛ(A, Λ). Namely, a left Λ-module A is a first syzygy if

A Course in the Theory of Groups

This is a detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the

Isomorphism of the Baumslag-Solitar groups

Necessary and sufficient conditions for the isomorphism of two groups, each defined by a single relation of the type a−1bma=bn, are obtained.

Metacyclic Invariants of Knots and Links

  • R. Fox
  • Mathematics
    Canadian Journal of Mathematics
  • 1970
To each representation ρ on a transitive permutation group P of the group G = π(S – k) of an (ordered and oriented) link k = k1 ∪ k2 ∪ … ∪ kμ in the oriented 3-sphere S there is associated an