Agemo subgroups of a p-group
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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.