C-group
From Groupprops
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
This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
VIEW: Definitions built on this | Facts about this: (facts closely related to C-group, all facts related to C-group) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions
You might be looking for: C-group (generating set sense); this term is used in relation to string C-groups
Definition
Symbol-free definition
A group is said to be a C-group if every subgroup in it is permutably complemented.
Definition with symbols
A group is said to be a C-group if for any subgroup of , there is a subgroup of such that is trivial and .
Relation with other properties
Stronger properties
Weaker properties
References
- A Course in the Theory of Groups by Derek J.S. Robinson