1
$\begingroup$

$G$ and $G \times G$ where $G = \Bbb Z_2 \times \Bbb Z_2 \times \Bbb Z_2 \times\cdots$

The answer says yes but I cannot figure out what homomorphism function I could use.

  • 1
    @Juan Liner: Okay, that was a bit snarky. Here's one way to think about it and so slap your forehead about how obvious it all was: Think of $G$ as being a product indexed by the natural numbers, one copy for every natural number. That is the same as having $G$ be a product indexed by the *even* natural numbers; or as having $G$ indexed by the *odd* natural numbers. Just the same, right? Well, now, when you look at $G\times G$, think of the *first* $G$ as being indexed by the even natural numbers, and the *second* as being indexed by the odd natural numbers. Then $G\times G$ is indexed by...2010-11-11

1 Answers 1