Okay, I'm really scratching my head here.(adsbygoogle = window.adsbygoogle || []).push({});

If an Abelian group A has three generators x,y,z and they are subject to three defining relations, say something like

x+y+z=0

x-y-z=0

2x-2y+3z=0

then I can solve for x,y,z and find A as a direct sum of cyclic groups, Z_x + Z_y + Z_z.

But what do I do if the three equations are not linearly independent? I get left with everything in terms of x and I can't just plug in the numbers.

Thanks,

N.

**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!

# Groups. I am stumped again.

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