Let G be an abelian group containing elements a and b of orders m and n respectively.

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Let G be an abelian group containing elements a and b of orders m and n respectively. Show that G contains an element whose order is the least common multiple of m and n.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 13, 2023 03:08 AM

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Let G be an abelian group containing elements a and b of orders m and n respectively.

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Since G is an abelian group we know that its elements commute with each other which means that for a...View the full answer

Algebra Graduate Texts In Mathematics 73

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