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If ( Q, + ) and ( Z, + ) be two infinite groups then
  • a)
    Every elements of quotient group Q/Z is of finite order.
  • b)
    Every elements of the subgroup  n are integers, p = fixed prime} of Q/Z is of finite order.
  • c)
    {Q , + ) is isomorphic to ( Q * , x ) {Q* = O - {0}}
  • d)
    ( R, + ) is isomorphic to (Ro, X).
Correct answer is option 'A,B'. Can you explain this answer?
Verified Answer
If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements o...





Hence, order of every element in G is finite. Option - C Let f : Q -> Q0 be a isomorphism Since x ∈ Q Such that f (x) = 2



Hence (Q , + ) and (Q0, x ) is not isomorphic.
Option -D 

But R has no element of order 2 and " under an isomorphism order of an element is preseived"
There cannot be any isomorphism between R and R0.
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Most Upvoted Answer
If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements o...





Hence, order of every element in G is finite. Option - C Let f : Q -> Q0 be a isomorphism Since x ∈ Q Such that f (x) = 2



Hence (Q , + ) and (Q0, x ) is not isomorphic.
Option -D 

But R has no element of order 2 and " under an isomorphism order of an element is preseived"
There cannot be any isomorphism between R and R0.
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If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements of quotient group Q/Zis of finite order.b)Every elements of the subgroupn are integers, p = fixed prime} of Q/Zis of finite order.c){Q , + ) is isomorphic to ( Q * , x ) {Q* = O - {0}}d)( R, + ) is isomorphic to (Ro, X).Correct answer is option 'A,B'. Can you explain this answer?
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If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements of quotient group Q/Zis of finite order.b)Every elements of the subgroupn are integers, p = fixed prime} of Q/Zis of finite order.c){Q , + ) is isomorphic to ( Q * , x ) {Q* = O - {0}}d)( R, + ) is isomorphic to (Ro, X).Correct answer is option 'A,B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements of quotient group Q/Zis of finite order.b)Every elements of the subgroupn are integers, p = fixed prime} of Q/Zis of finite order.c){Q , + ) is isomorphic to ( Q * , x ) {Q* = O - {0}}d)( R, + ) is isomorphic to (Ro, X).Correct answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ( Q, + ) and ( Z, + ) be two infinite groups thena)Every elements of quotient group Q/Zis of finite order.b)Every elements of the subgroupn are integers, p = fixed prime} of Q/Zis of finite order.c){Q , + ) is isomorphic to ( Q * , x ) {Q* = O - {0}}d)( R, + ) is isomorphic to (Ro, X).Correct answer is option 'A,B'. Can you explain this answer?.
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