# Cover for a group

From Groupprops

This article defines a property that can be evaluated for a subgroup familyView a complete list of properties of subgroup families

## Definition

A family of subgroups of a group is termed a **cover** for if it satisfies the following conditions:

- If , and , then
- if is a maximal subgroup of and has prime power order, then there exists such that and

## Properties

### Inductive cover

`Further information: inductive cover for a group`

A cover of a group is said to be inductive if given any subnormal subgroup of the group, intersecting each member of the cover with that subnormal subgroup gives a cover of that subgroup.

### Prime cover

`Further information: Prime cover for a group`