Recent content by vikas92

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    Only homomorphism from rationals to integers

    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
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    Only homomorphism from rationals to integers

    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...
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    Problem about normal subgroups

    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
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    Only homomorphism from rationals to integers

    Kindly see the attached image.i can't understand the step where he write f(x)=f(1+1+...+1)=xf(1).But the homomorphism is from <Q,.> to <Z,+>
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    Problem about normal subgroups

    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.
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    Easy Ratio Vector Question, but not sure if answer is wrong

    What you have done is right
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    Group theory finding order of element and inverse

    thanks i have got it if my solution to finding the order of ab correct or not
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    Group theory finding order of element and inverse

    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...
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    What Are the Best Physics Books and Online Resources for Self-Learning?

    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
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    What Is a Pseudochiral Carbon?

    thanks wax for ur support
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    What Is a Pseudochiral Carbon?

    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...
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    What Is a Pseudochiral Carbon?

    i am trying to understand what a pseudochiral carbon is? please help thanks in advance