Group that is finitely generated as a powered group for a set of primes

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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 G is termed a group that is finitely generated as a powered group for a set of primes if there exists a subset \pi (possibly empty, possibly finite, possibly infinite, possibly including all primes) such that G is a \pi-powered group and there is a finite subset S of G such that S is a generating set in the \pi-powered sense, i.e., there is no proper \pi-powered subgroup of G containing S.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian group that is finitely generated as a module over the ring of integers localized at a set of primes the group is also an abelian group Nilpotent group that is finitely generated as a powered group for a set of primes|FULL LIST, MORE INFO
nilpotent group that is finitely generated as a powered group for a set of primes |FULL LIST, MORE INFO