Subset has 2 Conjugates then Normal Subgroup
From ProofWiki
Theorem
Let $G$ be a group.
Let $S$ be a subset of $G$.
Let $S$ have exactly two conjugates in $G$.
Then $G$ has a proper nontrivial normal subgroup.
Proof
You can help Proof Wiki by expanding it.
To discuss it in more detail, feel free to use the talk page.
When this page/section has been completed, {{Stub}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
Sources
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 49 \alpha$
