(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

let G be a finite group, and let S and T be nonempty subsets.Prove either G=ST={st|s is in S, t is in T} or |G|>=|S|+|T|

2. Relevant equations

3. The attempt at a solution

So it is to prove G=ST, if |G|<|S|+|T|, which means also the intersection of S and T is nonempty (Note two smaller subsets can also have nonempty intersection, so |G|<|S|+|T| should have more properties than nonemptiness, but I fail to find one ). [tex]ST\subset G[/tex] is obvious. I want to prove the other direction by saying any g in G can be represented as g=st for some s,t, or [tex]s_{i}T[/tex] covers G.

This is what I 've done:

Let x be an element in both S and T. then x^2 is in ST. But x^2 can be outside S and T, So it is possible that [tex]x^{3}\notin ST[/tex], which seems to become useless...

Any hint 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: Finite group G=ST

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