Examples
- Every finite group with order coprime to all of the primes in the set P, or more generally any group such that the order of each element is coprime to all the primes in P is a P-root group.
- The special unitary groups and special orthogonal groups are root groups for all primes . For example, every element of except the identity is a rotation and has th roots. For the identity of has an infinite number of -roots for any prime, and the same is true of for .
- The orthogonal groups are -root groups for the set of all odd primes, but are not 2-root groups.
Read more about this topic: Root Group
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