Odd-order class two group

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: odd-order group and group of nilpotency class two
View other group property conjunctions OR view all group properties
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finite group and Baer Lie group
View other group property conjunctions OR view all group properties

Definition

An odd-order class two group is defined in the following equivalent ways:

  1. It is an odd-order group that is also a nilpotent group of class at most two.
  2. It is a finite group that is also a Baer Lie group.
  3. It is a finite nilpotent group, hence an internal direct product of its Sylow subgroups, each of which has class at most two.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
odd-order abelian group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
odd-order group |FULL LIST, MORE INFO
odd-order nilpotent group |FULL LIST, MORE INFO
group of nilpotency class two |FULL LIST, MORE INFO
Baer Lie group |FULL LIST, MORE INFO
Lazard Lie group (via Baer Lie group) Baer Lie group|FULL LIST, MORE INFO