(adsbygoogle = window.adsbygoogle || []).push({}); (Problem 49 from practice GRE Math exam:)Up to isomorphism, how many additive abelian groups G of order 16 have the property that x + x + x + x = 0 for each x in G?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 5

The answer is (D) 3, but I don't understand what the problem is asking, really, and I don't know what strategy I should take for this problem. My first guess was to just construct some groups having this property, but I think, on the actual exam, this strategy would take too long.

I was able to construct two groups, but I can't figure out what the third is.

[tex]G_1=\{0, 1, x, x+1, x^2, x^2+1, x^2+x, x^2+x+1, x^3, x^3+1, x^3+x, x^3+x+1, x^3+x^2, x^3+x^2+1, x^3+x^2+x, x^3+x^2+x+1\}[/tex]

[tex]G_2=\{0, 1, 2, 3, x, x+1, x+2, x+3, 2x, 2x+1, 2x+2, 2x+3, 3x, 3x+1, 3x+2, 3x+3\}[/tex]

Does anyone know what the third group is or have a better method for solving this problem?

Any suggestions / insights would be appreciated!

**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!

# Homework Help: Additive abelian group where x+x+x+x=0

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