Question 87
A group $(G,\cdot)$ has property $(P)$ if, for every automorphism $f$ of $G$, there exist automorphisms $g,h$ of $G$ such that $f(x)=g(x)\cdot h(x)$ for every $x\in G$. Prove:
a) Every group with $(P)$ is commutative.
b) Every finite commutative group of odd order has $(P)$.
c) No finite group of order $4n+2$, $n\in\mathbb N$, has $(P)$.
The order of a finite group is its number of elements.
a) Every group with $(P)$ is commutative.
b) Every finite commutative group of odd order has $(P)$.
c) No finite group of order $4n+2$, $n\in\mathbb N$, has $(P)$.
The order of a finite group is its number of elements.