The Group Properties Wiki (pre-alpha)

TIP: Beware of terminology local to the wiki

ABOUT US: Read our purpose statement and learn what makes us special

ALSO CHECK OUT: Commalg: The Commutative Algebra Wiki

Core-characteristic subgroup

From Groupprops

Jump to: navigation, search
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
View a complete list of subgroup properties|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: | | | | |
RANDOM TIP:The relation with other properties section lists stronger and weaker properties, along with links to proofs of the implications and non-implications. This helps give a feel of how the subgroup property relates to other properties.


Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this | Survey articles about this
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

Symbol-free definition

A subgroup of a group is termed core-characteristic if its normal core is a characteristic subgroup of the whole group.

Definition with symbols

A subgroup H of a group G is termed core-characteristic if the normal core HG of H in G is a characteristic subgroup of G.

Relation with other properties

Stronger properties

Conjunction with other properties

Any normal subgroup that is also core-characteristic, is characteristic.

Incomparable properties

Personal tools