Solution Found!
Prove that a group of order 175 must have normal subgroups of orders 7 and 25. (See
Chapter 58, Problem 58.13(choose chapter or problem)
QUESTION:
Prove that a group of order 175 must have normal subgroups of orders 7 and 25. (See Example 58.1.)
Questions & Answers
QUESTION:
Prove that a group of order 175 must have normal subgroups of orders 7 and 25. (See Example 58.1.)
ANSWER:Step 1 of 2
We have G to be a group of order 175. Now 175 can be factored as \(5^{2} \times 7\). Now, let us find out the number of Sylow 5-subgroups. The conditions to be satisfied are \(n_{5} \equiv 1(\bmod 5)\) and \(n_{5} \mid 7\). using these conditions we get \(n_{5}\) as 1.