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LSpice
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Bounding size of group by undernumber 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 VaughunVaughan-Lee and Zelmanov's survey, "Bounds in the restricted Burnside problem""Bounds in the restricted Burnside problem", I think they implicitly are invoking the claim that:

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

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

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 $G$)?

Bounding size of group by number 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 Vaughan-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 algebra over $\Bbb{F}_p$ with nilpotency class $C$, generated by elements $g_1,\dotsc,g_m$, then $\lvert G\rvert \le p^{m^C}$.

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

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Zach Hunter
Zach Hunter
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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 $G$)?