My understanding was that the product of two groups A and B will yield a group C for which the dimension of C is dim(A)*dim(B).(adsbygoogle = window.adsbygoogle || []).push({});

Now however, the author I'm reading defines the group product multiplication as:

(a1, b1) * (a2, b2) = (a1*a2, b1*b2), for a1,a2 in A and b1, b2 in B.

Does this give the same result for the dimension??

Lets take the example with A and B corresponding to the real numbers with addition as a group operation. This gives:

(x1, y1) + (x2, y2) = (x1+x2, y1+y2).... It looks like we have created the two dimensional plane! But dim(R)*dim(R) = 1 * 1 = 1. C should have dimension 1 not 2. :/

Please help me!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Product Groups and their dimensions

**Physics Forums | Science Articles, Homework Help, Discussion**