Could you show me how to do this in detail? Could you state any theorems and definition you used for this problem? 1. Show that the center Z(D2n) of the dihedral group of order 2n is non-trivial if andonly if n is even.

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Description: Could you show me how to do this in detail? Could you state any theorems and definition you used for this problem? 1. Show that the center Z(D2n) of the dihedral group of order 2n is non-trivial if andonly if n is even.

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Show that the center Z(D2n) of the dihedral group of order 2n is non-trivial if and only if n is even.

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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