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Suppose that a group contains elements of orders 1 through

Chapter 7, Problem 34E

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QUESTION:

Problem 34E

Suppose that a group contains elements of orders 1 through 10. What is the minimum possible order of the group?

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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.

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