# Odd-order class two group

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
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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
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## 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