Generalized 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
Definition with symbols
A group is termed a generalized Camina group if the following holds. Let be the center of and be the commutator subgroup of . Then, for , the coset is a single conjugacy class.
![{\displaystyle [G,G]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ddf7a724a331d1e12ffa6571ba246ebf08f1335)
![{\displaystyle g\notin [G,G]Z(G)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/572b98e2a787f617b561b8e2775e98a5eeae7e47)
![{\displaystyle g[G,G]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/15df5bbf2c210889b8b2bb9b0c705b3ed3ea6c50)