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Homelength function

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# length function

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

$\displaystyle L(e)$ | $\displaystyle=$ | $\displaystyle 0,$ | ||

$\displaystyle L(g)$ | $\displaystyle=$ | $\displaystyle L(g^{{-1}}),\quad\forall g\in G,$ | ||

$\displaystyle L(g_{1}g_{2})$ | $\displaystyle\leq$ | $\displaystyle L(g_{1})+L(g_{2}),\quad\forall g_{1},g_{2}\in G.$ |

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## Recent Activity

8:13 pm

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

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new correction: Closure properties on languages: DCFL not closed under reversal by babou

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new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag