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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Sign up to join this communityIs there a classification of finite nonabelian 2-groups of exponent 4?
What about, finite nonabelian 3-groups of exponent 3?
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 $3^{m + \binom{m}{2} + \binom{m}{3}}$.
What about, finite nonabelian 3-groups of exponent 3?
Those are all quotients of the Burnside group $B(m,3)$ for some value for $m$.