Solvable group generated by finitely many periodic elements

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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 solvable group generated by finitely many periodic elements is a group that is both a solvable group and a group generated by finitely many periodic elements.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite abelian group |FULL LIST, MORE INFO
finite nilpotent group |FULL LIST, MORE INFO
finite solvable group |FULL LIST, MORE INFO

Conjunction with other properties

Conjunction Other components of conjunction Explanation
finite solvable group could be finite group or periodic group

Incomparable properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated solvable group solvable and a finitely generated group any finitely generated torsion-free solvable group, such as the group of integers |FULL LIST, MORE INFO
solvable group generated by periodic elements any restricted direct power of infinitely many copies of a nontrivial finite solvable group will do |FULL LIST, MORE INFO
solvable group Solvable group generated by periodic elements|FULL LIST, MORE INFO
group generated by finitely many periodic elements |FULL LIST, MORE INFO
group generated by periodic elements Solvable group generated by periodic elements|FULL LIST, MORE INFO