Question

Let G be a group (not necessarily an Abelian group) of order 425. Prove that G must have an element of order 5. Note, Sylow Theorem is above us so we can't use it. We're up to Finite Orders. Thank you.

Answer #1

Statement of **Cauchy's theorem :** Let G be a
finite group and be a
prime number . If
divides the order of G then G has an element of order
.

Here G is a group of order 425 , since 5 divides 245 and 5 is a prime so G has an elements of order 5 .

.

.

The proof of Cauchys theorem is not that difficult , if you want proof of the theorem please comment .

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