Group admitting a partition into cyclic subgroups

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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
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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