Characteristicity is transitive
Revision as of 03:23, 1 March 2008 by Vipul (talk  contribs) (New page: {{trivial result}} {{subgroup metaproperty satisfaction}} ==Statement== ===Propertytheoretic statement=== The subgroup property of being characteristic ...)
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This article gives the statement, and possibly proof, of a subgroup property satisfying a subgroup metaproperty
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Property "Page" (as page type) with input value "{{{property}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
Property "Page" (as page type) with input value "{{{metaproperty}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.
Contents
Statement
Propertytheoretic statement
The subgroup property of being characteristic satisfies the subgroup metaproperty of being transitive.
Verbal statement
A characteristic subgroup of a characteristic subgroup is characteristic in the whole group.
Symbolic statement
Let be a characteristic subgroup of , and a characteristic subgroup of . Then, is a characteristic subgroup of .
Proof
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References
Textbook references
 Book:Alperinbell^{More info}, Page 17