Definition:Boolean Group

Theorem

Let $\struct {G, \circ}$ be a group.

Then $\struct {G, \circ}$ is a Boolean group if and only if all its elements, other than the identity, have order $2$.

Also see

• Boolean Group is Abelian
• Group Element is Self-Inverse iff Order 2

• Results about Boolean groups can be found here.

Source of Name

This entry was named for George Boole.

Sources

• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 1$: Exercise $8$