Camina 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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Definition
Symbol-free definition
A group is termed a Camina group if every coset of the derived subgroup other than the commutator subgroup itself, forms exactly one conjugacy class.
Definition with symbols
A group is termed a Camina group if for every , the coset is a conjugacy class.
![{\displaystyle g\notin [G,G]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2e449ced04b7ba230f95d314338566308bae268)
![{\displaystyle g[G,G]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/15df5bbf2c210889b8b2bb9b0c705b3ed3ea6c50)
Relation with other properties
Stronger properties
- Perfect group
- Abelian group
- Extraspecial group: For full proof, refer: extraspecial implies Camina