Plz Let G be a finite abelian group, and let 7 be the product of the elementsof G.(a) Show that has order 1 or 2.(b) Give an example of a group G of even order in which is the identity.(c) Give an example of a group G of even order in which has order 2.(d) Show that has order 2 iff G has a unique element of order 2.

Answered: the product of the elements is the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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the product of the elements is the identity. 7 has order 2. of order 2.