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Variations on a Theme: \(A_4\) Definitely Has no Subgroup of Order Six!

The authors present 11 different proofs that the alternating group\( A_4\) has no subgroup of order 6, and hence that the converse of Lagrange's theorem is false.

Old Node ID: 
3391
MSC Codes: 
20-XX
Author(s): 
<p>Michael Brennan (Cork Institute of Technology Ireland) and Des Machale (University College Ireland)</p>
Publication Date: 
Monday, February 8, 2010
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
February, 2000
Subject(s): 
Algebra and Number Theory
Abstract Algebra
Groups
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Publish Page: 
Furnished by JSTOR: 
Rating Count: 
5.00
Rating Sum: 
15.00
Rating Average: 
3.00
Applicable Course(s): 
4.2 Mod Algebra I & II
Modify Date: 
Monday, February 8, 2010
Average: 3 (5 votes)

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