(a) What are the elementary divisors of the group Z 2 Z 9 Z 35 ; what...
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(a) What are the elementary divisors of the group Z2⊕Z9⊕Z35; what are its invariant factors? Do the same for Z26⊕Z42⊕Z49⊕Z200⊕Z1000.
(b) Determine up to isomorphism all abelian groups of order 64; do the same for order 96.
(c) Determine all abelian groups of order n for n ≤ 20.
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ANSWER a For the group Z2Z9Z35 we have the following prime factorizations 2 21 9 32 35 5 7 The elementary divisors of the group are then the distinct prime powers that divide the group order which are ...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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