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Is there a classification of finite nonabelian 2-groups of exponent 4?

What about, finite nonabelian 3-groups of exponent 3?

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There is no classification of finite groups of exponent 4. You might find this paper interesting - it contains lots of information about how the group Burnside group $B(m,4)$ grows (all $m$-generator exponent-4 groups are quotients of this group).

There is also no classification of finite groups of exponent 3. However it is known that these groups must be $2$-Engel and class three. Furthermore in this case the precise size of the corresponding Burnside group is known: $B(m,3)$ is a finite group of size $3^{m + \binom{m}{2} + \binom{m}{3}}$.

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  • $\begingroup$ Please activate the link of "this paper". Many thanks. $\endgroup$ – user100452 Oct 30 '16 at 10:19
  • $\begingroup$ Access was denied on the link: was it a paper of M. Vaughn-Lee, who has worked a lot on such groups? $\endgroup$ – Geoff Robinson Oct 30 '16 at 11:41
  • $\begingroup$ @user100452, Dropbox seems to have changed its policy on link sharing, and I can't figure out how to make the paper public. Please email me -- my details are on my user page -- and I'll happily send you a copy of the paper. $\endgroup$ – Nick Gill Oct 31 '16 at 9:02
  • $\begingroup$ @GeoffRobinson, It's a paper by Avinoam Mann: On the orders of groups of exponent 4. $\endgroup$ – Nick Gill Oct 31 '16 at 9:04
  • $\begingroup$ @NickGill : Thanks.. Vaughn-Lee has done a lot of work on groups of exponent $4$. $\endgroup$ – Geoff Robinson Oct 31 '16 at 9:47
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What about, finite nonabelian 3-groups of exponent 3?

Those are all quotients of the Burnside group $B(m,3)$ for some value for $m$.

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    $\begingroup$ Tom, you beat me by 1 minute!! $\endgroup$ – Nick Gill Nov 14 '12 at 8:52
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    $\begingroup$ But your answer is more complete than mine :) $\endgroup$ – Tom De Medts Nov 14 '12 at 12:55

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