# Group admitting a partition into cyclic subgroups

From Groupprops

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A **group admitting a partition into cyclic subgroups** is defined as a group that can be expressed as a union of cyclic subgroups any two of which have trivial intersection. In other words, it admits a Partition of a group (?) where all the parts are cyclic subgroups.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Cyclic group | |FULL LIST, MORE INFO | |||

Elementary abelian group | |FULL LIST, MORE INFO | |||

Group of prime exponent | |FULL LIST, MORE INFO | |||

Dihedral group | |FULL LIST, MORE INFO | |||

Generalized dihedral group for an elementary abelian group | ||||

Subgroup of the affine group over a finite field |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Group admitting a partition into abelian subgroups |