Let the order of group G =8, show that G must have an element of order 2.
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 the order of group G =8, show that G must have an element of order 2.
Expert Solution
Step 1
Let G be a group and O(G)=8
Also Let be an arbitrary element other than identity.
Then the possible order of element a be 2,4,8
By the consequences of Lagrange's Theorem.
Suppose G be a cyclic group then there a generator a such that
There exist an element whose order will be 2 because
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