Question:
Prove that any group of order 175 is Abelian.
The solution:
I am unable to understand why the intersection of the normal subgroups is the trivial intersection.
Any help is appreciated.
2026-04-21 16:04:37.1776787477
Group of order 175 is Abelian
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The intersection of two groups is a group. By Lagrange's theorem, the order of a subgroup of a group divides the order of the group. Thus $|P\cap Q| \mid |P|=7$ and $|P\cap Q| \mid |Q|=5 \text{ or }25$ thus $|P\cap Q|=1$ and...