C-group: Difference between revisions

Revision as of 01:22, 9 January 2008

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

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 $H K = G$ .

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

@@ Line 11: / Line 11: @@
 ===Definition with symbols===
-A group <math>G</math> is said to be a '''C-group''' if for any subgroup <math>H</math> of <math>G</math>, there is a subgroup <math>K</math of <math>G</math> such that <math>H</math> &cap; <math>K</math> is trivial and <math>HK = G</math>.
+A group <math>G</math> is said to be a '''C-group''' if for any subgroup <math>H</math> of <math>G</math>, there is a subgroup <math>K</math> of <math>G</math> such that <math>H \cap K</math> is trivial and <math>HK = G</math>.
 ==Relation with other properties==