@article {
author = {Prajapati, S. K. and Sarma, R.},
title = {On group equations},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {2},
pages = {315-324},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = { Suppose $f$ is a map from a non-empty finite set $X$ to a finite group $G$. Define the map $\zeta^f_G: G\longrightarrow \mathbb{N}\cup \{0\}$ by $g\mapsto |f^{-1}(g)|$. In this article, we show that for a suitable choice of $f$, the map $\zeta^f_G$ is a character. We use our results to show that the solution function for the word equation $w(t_1,t_2,\dots,t_n)=g$ ($g\in G$) is a character, where $w(t_1,t_2,\dots,t_n)$ denotes the product of $t_1,t_2,\dots,t_n,t_1^{-1},t_2^{-1},\dots,t_n^{-1}$ in a randomly chosen order. },
keywords = {finite groups,word equations,group characters},
url = {http://bims.iranjournals.ir/article_611.html},
eprint = {http://bims.iranjournals.ir/article_611_12adc2b3a8b377f26a5c5fcccd2a6e5e.pdf}
}