Linear norm

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This is the wiki page for understanding seminorms of linear growth on a group [math]G[/math] (such as the free group on two generators). These are functions [math]\| \|: G \to [0,+\infty)[/math] that obey the triangle inequality

[math]\|xy\| \leq \|x\| + \|y\|[/math]

and the linear growth condition

[math] \|x^n \| = |n| \|x\| [/math]

for all [math]x,y \in G[/math] and [math]n \in {\bb Z}[/math].


Key lemmas