Hi I have this problem, and I cant seem to get it. It is not for a grade just for study practice. Let me know if you can do it. Thanks...
Let G be a group, |G|= for a p a prime and (p,m) =1 and H G with |H|= . If K G with |K|= and HK = KH, then show K H.
Need to show K is a subgroup of H. Thanks again.
Okay well maybe if I can explain what I have so far, maybe It will help.
HK= HK implies that HK G
I also know that the |HK| = |H||K|/|H K|
I also know that |G| = |H| [G:H] which seems to imply that [G:H] = m by lagrange
Also I know that |HK| divides |G| by lagrange
Im thinking I have all the pieces put I dont know how to put them together right.