Difference between revisions of "Characteristicity is transitive"
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==References==  ==References==  
===Textbook references===  ===Textbook references===  
−  * {{booklinkDummitFoote}}, Page 135, Page 137 (Problem 8(b))  +  * {{booklinkstatedDummitFoote}}, Page 135, Page 137 (Problem 8(b)) 
−  * {{booklinkAlperinBell}}, Page 17, ''Lemma 4''  +  * {{booklinkstatedAlperinBell}}, Page 17, ''Lemma 4'' 
−  * {{booklinkRobinsonGT}}, Page 28, ''Characteristic and Fully invariant subgroups'', 1.5.6(ii)  +  * {{booklinkstatedRobinsonGT}}, Page 28, ''Characteristic and Fully invariant subgroups'', 1.5.6(ii) 
Revision as of 23:18, 9 May 2008
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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.
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
PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]References
Textbook references
 Abstract Algebra by David S. Dummit and Richard M. Foote, 10digit ISBN 0471433349, 13digit ISBN 9780471433347, ^{More info}, Page 135, Page 137 (Problem 8(b))
 Groups and representations by Jonathan Lazare Alperin and Rowen B. Bell, ISBN 0387945261, ^{More info}, Page 17, Lemma 4
 A Course in the Theory of Groups by Derek J. S. Robinson, ISBN 0387944613, ^{More info}, Page 28, Characteristic and Fully invariant subgroups, 1.5.6(ii)