M  be a group (not necessarily an Abelian group) of order 387. Prove that M  must have an element of order 3.

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 M  be a group (not necessarily an Abelian group) of order 387. Prove that M  must have an element of order 3.

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