Complemented characteristic subgroup

From Groupprops
Revision as of 20:03, 18 May 2009 by Vipul (talk | contribs) (Created page with '{{subgroup property conjunction|permutably complemented subgroup|characteristic subgroup}} ==Definition== ===Symbol-free definition=== A subgroup of a group is termed ...')
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutably complemented subgroup and characteristic subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a complemented characteristic subgroup if it satisfies the following equivalent conditions:

  1. It is a characteristic subgroup as well as a permutably complemented subgroup.
  2. It is a characteristic subgroup as well as a lattice-complemented subgroup.
  3. It is a characteristic subgroup as well as a complemented normal subgroup, i.e., it occurs as the normal subgroup part in an internal semidirect product.

Relation with other properties

Stronger properties

Weaker properties