Skip to main content
1 of 2
Zach Hunter
  • 3.5k
  • 2
  • 11
  • 24

Bounding size of group by under of generators, order of elements, and nilpotency class (Restricted Burnside's)

I have been looking at some papers on the "restricted Burnside problem". On page 4 of Vaughun-Lee and Zelmanov's survey, "Bounds in the restricted Burnside problem", I think they implicitly are invoking the claim that:

If $G$ is a Lie alegebra over $\Bbb{F}_p$ with nilpotency class $C$, generated by elements $g_1,\dots,g_m$, then $|G| \le p^{m^C}$.

How does one prove a claim? Is there a nice combinatorial reason for this (I want to guess that this translates to a nice bound on the dimension of $G$)?

Zach Hunter
  • 3.5k
  • 2
  • 11
  • 24