Factorizations in finite groups

conjugate factorizations of finite groups

in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

On Minimal Length Factorizations of Finite Groups

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...

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.