# Agemo subgroups of a p-group

From Groupprops

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## Definition

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.

## Subgroup properties satisfied

All the agemo subgroups are fully invariant subgroups, in fact, they're all verbal subgroups.