Group of prime exponent

Definition
A group of prime exponent is a group whose exponent is a prime number. If $$p$$ is a prime number, a group of exponent $$p$$ is a (nontrivial) group in which every element has order $$p$$.

Particular cases
For related information, see the Burnside problem. Note that for those primes $$p$$ for which the Burnside problem has an answer of No, it is possible to have an infinite group of exponent $$p$$ with a finite generating set. However, there will still be many finite groups of interest with exponent $$p$$ and a finite generating set.

Stronger properties

 * Elementary Abelian group