AxB

• Oct 8th 2011, 12:00 PM
dwsmith
AxB
Let A, B be groups. Prove that the following sets are subgroups of AxB:

$\{a\times e:a\in A\}$

Not sure how to do this with ordered pairs.
• Oct 8th 2011, 12:24 PM
Drexel28
Re: AxB
Quote:

Originally Posted by dwsmith
Let A, B be groups. Prove that the following sets are subgroups of AxB:

$\{a\times e:a\in A\}$

Not sure how to do this with ordered pairs.

Well, you can do it directly, but let me ask you this. The projection $\pi:A\times B\to A: (a,b)\mapsto a$ is a homomorphism by definition, right? What is its kernel?