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Suppose that a group contains elements of orders 1 through
Chapter 7, Problem 34E(choose chapter or problem)
QUESTION:
Problem 34E
Suppose that a group contains elements of orders 1 through 10. What is the minimum possible order of the group?
Questions & Answers
QUESTION:
Problem 34E
Suppose that a group contains elements of orders 1 through 10. What is the minimum possible order of the group?
ANSWER:
Step 1 of 2
Let G be a group that contains elements of orders 1 through 10.
To find the minimum possible order of the group.
Since, G contains elements of orders 1 through 10, by Lagrange’s theorem, the order of the group must be divisible by each positive integer 1 through 10.