Group generated by involutions
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Definition
Symbol-free definition
A group is said to be generated by involutions if it has a generating set all whose elements are involutions (elements of order two).
Typical examples are triangle groups, and various reflection groups.
Relation with other properties
Stronger properties
- Triangle group
- Real special orthogonal group: This is the content of the Cartan-Dieudonne theorem
- Finitary symmetric group, in particular the symmetric group on a finite set. For full proof, refer: Transpositions generate the finitary symmetric group
- Finite simple non-Abelian group
Weaker properties
Metaproperties
Quotients
This group property is quotient-closed, viz., any quotient of a group satisfying the property also has the property
View a complete list of quotient-closed group properties
Direct products
This group property is finite direct product-closed, viz the direct product of a finite collection of groups each having the property, also has the property
View other finite direct product-closed group properties