conjugate factorizations of finite groups

On Minimal Length Factorizations of Finite Groups

Conjugate Graphs of Finite Groups

In this paper we introduce the conjugate graph ΓG associated to a nonabelian group G with vertex set G\Z(G) such that two distinct vertices join by an edge if they are conjugate. We show if ΓG ∼= ΓS , where S is a finite nonabelian simple group which satisfy Thompson’s conjecture, then G ∼= S. Further, if central factors of two nonabelian groups H and G are isomorphic and |Z(G)| = |Z(H)|, then ...

Spectral Sets and Factorizations of Finite Abelian Groups

A spectral set is a subset 0 of R with Lebesgue measure 0<+(0)< such that there exists a set 4 of exponential functions which form an orthogonal basis of L(0). The spectral set conjecture of B. Fuglede states that a set 0 is a spectral set if and only if 0 tiles R by translation. We study sets 0 which tile R using a rational periodic tile set S=Z+A, where A (1 N1)Z_ } } } _(1 Nn)Z is finite. We...

Partitionable graphs arising from near-factorizations of finite groups

In 1979, two constructions for making partitionable graphs were introduced in (by Chv2 atal et al. (Ann. Discrete Math. 21 (1984) 197)). The graphs produced by the second construction are called CGPW graphs. A near-factorization (A; B) of a %nite group is roughly speaking a non-trivial factorization of G minus one element into two subsets A and B. Every CGPW graph with n vertices turns out to b...

Factorizations of Primitive Permutation Groups

Finite Group Factorizations and Braiding

We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group into two subgroups. The representations of the quantum double are described by a notion of bicrossed bimodules, generalising the cross modules of Whitehead. We also show that self-duality structures for the bicrossproduct ...