Camina group
This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]
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 termed a Camina group if every coset of the commutator 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)