Group of prime exponent
The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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|Value of prime ?||What can we say about groups of exponent|
|2||must be elementary abelian. See exponent two implies abelian|
|3||must be 2-Engel and class three. Also, if it has a generating set of finite size , it must be a quotient of the Burnside group , which is a finite group of size|
|5||no bound on nilpotency class. Unknown whether finite generating set forces the group to be finite.|
For related information, see the Burnside problem. Note that for those primes for which the Burnside problem has an answer of No, it is possible to have an infinite group of exponent with a finite generating set. However, there will still be many finite groups of interest with exponent and a finite generating set.