Solvable p-group

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: p-group and solvable group
View other group property conjunctions OR view all group properties

Definition

Let p be a prime number. A solvable p-group is a p-group (see p-group -- every element has order a power of p) that is also a solvable group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group of prime power order finite p-group prime power order implies nilpotent
abelian p-group
nilpotent p-group
locally finite solvable p-group