Iterated agemo subgroup of p-group

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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