- #1

annoymage

- 362

- 0

## Homework Statement

if H and K are arbitrary subgroup of G, prove that HK=KH iff HK is a subgroup of G

## Homework Equations

n/a

## The Attempt at a Solution

no problem to prove => direction

for <= i can prove KH is a subset of HK

only i got troubled to show HK ia subset of KH

x in HK

x=hk for some h in H ,k in K

i manipulate it many ways and always got the form x=khk for some h in H ,k in K

HELP, and sorry no latex ,i'm very buzy now ;P