Thanks for your reply.Perhaps it is serving as counterexample to what the question was given.In some other book the same question was there with <Q,+> instead of <Q,.>
.Maybe the solution provided by the author is wrong
Sorry for bad image quality.
Show that only homomorphism from the group <Q*,.> to <Z,+> is the zero homomorphism where Q*=Q-{0}
Solution
Let 0≠f be a homomorphism from <Q*,.> to <Z,+>
Let f(1)=n\inZ. Suppose f(1)=0
Then f(x)=f(1+1+...+1) if x>0,x\inZ
=x f(1)=0
This is the step I...
x=bc \Rightarrow a-1bac\inBC
Also a-1bca\inBC Now a-1b=a1 for some a1\inA\Rightarrowa1ca\inBC
a1(aa-1)ca\inBC
(a1a)c1\inBC for some c1\inC
a2c1\inBC
Cant still figure out
Homework Statement
If A,B and C are normal subgroups of G where B\subseteqA show that
A\bigcapBC=B(A\bigcapC)
Homework Equations
The Attempt at a Solution
Let x\inA\bigcapBC.then x\inA and x\inBC
Now as B\subseteqA thus BA=A.thus left side is BA\bigcapBC
Dont know how to proceed.
Homework Statement
Let a and b be elements of a group,with a^2=e , b^6=e and a.b=b^4.a find its order and express its inverse in form of a^m.b^n
Homework Equations
The Attempt at a Solution
(ab)^2=(ab)(ab)=(ab)(b^4.a)=a(b^5)a
(ab)^3=a(b^5)a(ab)=a(b^5)(a^2)b=a(b^6)=ae=a
it...
start learning some trig and then some calculus.then u may start reading some physics books like young and freedman's university physics or resnick halladay.also mit lectures by walter lewin will be helpful
i know what a chiral carbon is and also what chiral means but do not know wat a pseudo chiral carbon is.actually def. of pseudo chiral carbon is not there in our course book but it is mentioned in our syllabus and while attempting some questions from some practice book there was a ques that how...