Jensen's functional equation on the symmetric group $\bold{S_n}$

Details Jensen's functional equation on the symmetric group $\bold{S_n}$ Jensen's functional equation on the symmetric group $\bold{S_n}$

2011-03-30

arxiv.org/abs/1103.5955v2

Mathematics

Group Theory

8 pages, Abstract changed, the proof of Proposition 2.1 and Lemma 2.4 changed (minor), one reference added, final version, to

Scientific paper

10.1007/s00010-011-0089-7

Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(xy^{-1}) = 2f(x)$ and $f(xy)+f(y^{-1}x) = 2f(x)$, where $f$ is a map from a multiplicative group $G$ into an abelian additive group $H$. In a series of papers \cite{Ng1}, \cite{Ng2}, \cite{Ng3}, C. T. Ng has solved these functional equations for the case where $G$ is a free group and the linear group $GL_n(R)$, $R=\z,\r$, a quadratically closed field or a finite field. He has also mentioned, without detailed proof, in the above papers and in \cite{Ng4} that when $G$ is the symmetric group $S_n$ the group of all solutions of these functional equations coincides with the group of all homomorphisms from $(S_n,\cdot)$ to $(H,+)$. The aim of this paper is to give an elementary and direct proof of this fact.

Affiliated with

Also associated with

No associations

Rating

Jensen's functional equation on the symmetric group $\bold{S_n}$ 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 Jensen's functional equation on the symmetric group $\bold{S_n}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Jensen's functional equation on the symmetric group $\bold{S_n}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-569441