# Iterated agemo subgroup of p-group

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

Suppose $p$ is a prime number and $G$ is a p-group. A subgroup $H$ of $G$ is an iterated agemo subgroup of $G$ if there exists a sequence $a_1,a_2,\dots,a_r$ such that:

$H := \mho^{a_1}(\mho^{a_2}(\mho^{a_3}(\dots(\mho^{a_r}(G)))\dots)$.

## Relation with other properties

### Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
agemo subgroup of p-group iterated agemo subgroup not implies agemo subgroup

### Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
verbal subgroup of p-group iterated agemo implies verbal verbal not implies iterated agemo