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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let G be a finite abelian group, and let 7 be the product of the elements of 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.
Transcribed Image Text:Let G be a finite abelian group, and let 7 be the product of the elements of 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.
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