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Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.
  • a)
  • b)
    S3
  • c)
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let G be the group with the generators a and b given byG = {(a,b)|&sig...
Clearly G ≈ D4
Also |z(Dn)| = 2 if n is even and |z(Dn)| = 1 if n is odd
Also G is non abelian
⇒ G/Z(G) can not be cyclic =G/Z(G) ≈ 
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Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.a)b)S3c)d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.a)b)S3c)d)none of theseCorrect answer is option 'C'. 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 Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.a)b)S3c)d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be the group with the generators a and b given byG = {(a,b)|σ(a) = 4,σ(b) = 2, ba = a-1b}. Let Z(G) denotes the centre of G. Then G/Z(G) is isomorphic to.a)b)S3c)d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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