2-powered nilpotent group

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: 2-powered group and nilpotent group
View other group property conjunctions OR view all group properties

Definition

A group is termed a 2-powered nilpotent group if it is both a 2-powered group (i.e., every element has a unique square root) and a nilpotent group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
rationally powered nilpotent group |FULL LIST, MORE INFO
Baer Lie group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
2-powered group |FULL LIST, MORE INFO
2-torsion-free nilpotent group |FULL LIST, MORE INFO
nilpotent group |FULL LIST, MORE INFO