On conjugacy classes and derived length

Details On conjugacy classes and derived length On conjugacy classes and derived length

2009-05-08

arxiv.org/abs/0905.1342v2

Mathematics

Group Theory

5 pages. Correction of typos and other misfortunes

Scientific paper

Let $G$ be a finite group and $A$, $B$ and $D$ be conjugacy classes of $ G$ with $D\subseteq AB=\{xy\mid x\in A, y\in B\}$. Denote by $\eta(AB)$ the number of distinct conjugacy classes such that $AB$ is the union of those. Set ${\bf C}_G(A)=\{g\in G\mid x^g=x {for all} x\in A\}$. If $AB=D$ then ${\bf C}_G(D)/({\bf C}_G(A)\cap{\bf C}_G(B))$ is an abelian group. If, in addition, $G$ is supersolvable, then the derived length of ${\bf C}_G(D)/({\bf C}_G(A)\cap{\bf C}_G(B))$ is bounded above by $2\eta(AB)$.

Affiliated with

Also associated with

No associations

Rating

On conjugacy classes and derived length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On conjugacy classes and derived length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On conjugacy classes and derived length will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688750