C-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
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 G is said to be a C-group if for any subgroup H of G, there is a subgroup K of G such that H \cap K is trivial and HK = G.

Relation with other properties

Stronger properties

Weaker properties

References

  • A Course in the Theory of Groups by Derek J.S. Robinson