# Quotient-iterated omega subgroup of group of prime power order

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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 is a prime number and is a finite -group, so is a group of prime power order. A subgroup of is termed a **quotient-iterated omega subgroup** of if there exist nonnegative integers and normal subgroups of , where is trivial, , and .

## Relation with other properties

### Stronger properties

property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|

Omega subgroup of group of prime power order |

### Weaker properties

property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|

Fully invariant subgroup of group of prime power order | ||||

Intermediately fully invariant subgroup of group of prime power order |