Gamma-1-2 group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
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 a group if every element of the group belongs to a pair of mates of which at least one element is an involution (viz has order two).
Relation with other properties
Stronger properties
- Suzuki group
- Simple Chevalley group over a finite field of odd order
Weaker properties
References
- Two-generator groups by J. L. Brenner and James Wiegold, Michigan Math. J. 22, 1975, Pg. 53-64
- Finite groups with a special 2-generator property by Tuval Foguelm Pacific Journal of Mathematics, 170, no. 2 (95), 483-496.