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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 14E: 14. Let be an abelian group of order where and are relatively prime. If and , prove that .

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Let G be a finite abelian group and let
a, b E G. Let m = ord(a) and b = ord
(b). Let | = |cm(m, n). Then there exists
Some c E G such that ord (c) = L.

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