From the blog
-
Let G be a group such that Aut(G) is cyclic and not trivial. Then Aut(G) is finite and his order is even.
Since Aut(G) is cyclic then Inn(G) is cyclic so G/Z(G) is cyclic which implies G being abelian. Let us first show that Aut(G) has an…
-
Let f ∈ ℚ[X] irreducible, then f doesn’t have multiple roots in ℂ
To prove the assertion suppose f=a₀+a₁X+…+anXⁿ and let α be a multiple root of f. Consider g=an⁻¹f . Then g is irreducible, monic and has…
-
There is no non-constant f ∈ ℤ[X]: f(x) is prime for every integer x
Suppose by contradiction that there exists a non-constant polynomial f with coefficients in ℤ such that f(x) is prime for every integer x. Then there…
Marco Damele 