Group generated by involutions

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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


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

Weaker properties



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