Tagged: group of integers
Group Theory

06/07/2017

by
Yu
· Published 06/07/2017
· Last modified 06/08/2017

Problem 443
Let $A=B=\Z$ be the additive group of integers.
Define a map $\phi: A\to B$ by sending $n$ to $2n$ for any integer $n\in A$.

(a) Prove that $\phi$ is a group homomorphism.

(b) Prove that $\phi$ is injective.

(c) Prove that there does not exist a group homomorphism $\psi:B \to A$ such that $\psi \circ \phi=\id_A$.

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Group Theory

11/02/2016

by
Yu
· Published 11/02/2016
· Last modified 06/21/2017

Problem 163
Let $\Z$ be the additive group of integers. Let $f: \Z \to \Z$ be a group homomorphism.
Then show that there exists an integer $a$ such that
\[f(n)=an\]
for any integer $n$.

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