Gamma-1-2 group

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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

Definition

Symbol-free definition

A group is said to be a \Gamma_1^{(2)} 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

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.

External links