let a,b \epsilon H and a,b \epsilon K .Then a*b \epsilon H and a*b \epsilon K .Let a \epsilon H and a \epsilon K .Then a^{-1} \epsilon H and a^{-1} \epsilon K .
For H to be a subgroup of G existence of inverse is sufficient condition.Because if a \epsilon\ G then a^{-1}
\epsilon G due to existence of inverse.But since H is closed a*a^{-1} \epilson \ H.Therefore e \epilson H .
Now, since H is a finite group there must exist an n such that a^n=e...
This problem is from the first set of problems in Abstract Algebra(I N Herstein).Only the definitions of a group and abelian group are to be used in solving this problem and nothing else ,for these are the only things I came across in this book till now.
Homework Statement
Show that a group of order 5 must be abelian.Please don't use Langrage's Theorem.
Homework Equations
The Attempt at a Solution
I have been working on this problem for a while and I can't seem to
get anywhere on it. Please help.
You can use Fundamentals of Physics by Haliday and Resnick.There is a chapter on special relativity and few chapters on basic quantum mechanics.Also there are plenty of exercises of varying difficulty level.If you want something of higher level then you must try the Berkeley Physics Course.I...
I'm an undergraduate student studying computer science.I am interested in doing some research in discrete mathematics or theoretical computer science.Can anyone tell some interesting research topics or open problems on which i can work on?