Agemo subgroups of a p-group
Let be a prime number and be a -group. For any nonnegative integer , the agemo subgroup of is defined as:
In other words, it is the subgroup generated by all the powers.
If the exponent of is , then (and any higher agemo subgroup) is trivial, and all previous are nontrivial.
The subgroups form a descending chain.
We can also consider agemo subgroups of a pro-p-group.