Following the idea suggested in Exercise 26, let m and n be relatively prime positive integers. Show

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Following the idea suggested in Exercise 26, let m and n be relatively prime positive integers. Show that if there are (up to isomorphism) r abelian groups of order m ands of order n, then there are (up to isomorphism) rs abelian groups of order mn.

Data from exercise 26

How many abelian groups (up to isomorphism) are there of order 24? of order 25? of order (24)(25)?

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A First Course In Abstract Algebra

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7th Edition

Authors: John Fraleigh

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Question Posted: Dec 30, 2022 05:11 AM

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Following the idea suggested in Exercise 26, let m and n be relatively prime positive integers. Show

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Because there are no primes that divide both m and n any abelian group of order mn is isomorphic to ...View the full answer

A First Course In Abstract Algebra

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