Answered: Suppose that |a| and |b| are elements…

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Suppose that |a| and |b| are elements of a group and a and b commute.If |a| = 5 and |b| = 16, prove that |ab| = 80.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 18E: Let a and b be elements of a group G. Prove that G is abelian if and only if (ab)2=a2b2.

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Question

Suppose that |a| and |b| are elements of a group and a and b commute.
If |a| = 5 and |b| = 16, prove that |ab| = 80.

Expert Solution

Step 1

Given, a and b are elements of a group such that a and b commute.
Also, given |a| = 5 and |b| = 16. Then, we have to prove that |ab| = 80.

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Solved in 2 steps

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