C-group

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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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.
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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

• SC-group

Weaker properties

• K-group

References

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