# length function

Let $G$ be a group. A length function on $G$ is a function $L\colon G\to\mathbb{R}^{+}$ satisfying:

 $\displaystyle L(e)$ $\displaystyle=$ $\displaystyle 0,$ $\displaystyle L(g)$ $\displaystyle=$ $\displaystyle L(g^{-1}),\quad\forall g\in G,$ $\displaystyle L(g_{1}g_{2})$ $\displaystyle\leq$ $\displaystyle L(g_{1})+L(g_{2}),\quad\forall g_{1},g_{2}\in G.$
Title length function LengthFunction 2013-03-22 13:41:29 2013-03-22 13:41:29 mhale (572) mhale (572) 6 mhale (572) Definition msc 20-02