No two of D 6 , A 4 , and T are isomorphic, where T is the
Question:
No two of D6, A4, and T are isomorphic, where T is the group of order 12 described in Proposition 6.4 and Exercise 5.
Data from in exercise 5
(a) Show that there is a nonabelian subgroup T of S3 X Z4 of order 12 generated by elements a,b such that |a| = 6, a3 = b2, ba = a-1b.(b) Any group of order 12 with generators a,b such that lal = 6, a3 = b2, ba = a-1b is isomorphic to T.
Transcribed Image Text:
Proposition 6.4. There are (up to isomorphism) exactly three distinct nonabelian groups of order 12: the dihedral group De, the alternating group A, and a group T generated by elements a,b such that |a| = 6, b² = a³, and ba = a-¹b.
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Based on Exercise 5 and Proposition 64 we have three nonabelian groups of order 12 Dihedral group De ...View the full answer
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Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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