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If H be normal in G such that 0 (H) and  are co-prime then 
  • a)
    H is only subgroup of G of 0(H)
  • b)
    H is trivial subgroup of G
  • c)
    G have exactly normal 2 non-trivial normal subgroups of given order
  • d)
    H ≠ φ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If H be normal in G such that 0 (H) andare co-prime thena)H is only su...
Let 0(H) = m
Suppose K is a subgroup of G of order m
Since H is normal 
Thus 0(HK)|0(G)
Thus d = m and hence
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Most Upvoted Answer
If H be normal in G such that 0 (H) andare co-prime thena)H is only su...
Let 0(H) = m
Suppose K is a subgroup of G of order m
Since H is normal 
Thus 0(HK)|0(G)
Thus d = m and hence
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If H be normal in G such that 0 (H) andare co-prime thena)H is only subgroup of G of 0(H)b)H is trivial subgroup of Gc)G have exactly normal 2 non-trivial normal subgroups of given orderd)H ≠ φCorrect answer is option 'A'. Can you explain this answer?
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If H be normal in G such that 0 (H) andare co-prime thena)H is only subgroup of G of 0(H)b)H is trivial subgroup of Gc)G have exactly normal 2 non-trivial normal subgroups of given orderd)H ≠ φCorrect answer is option 'A'. 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 H be normal in G such that 0 (H) andare co-prime thena)H is only subgroup of G of 0(H)b)H is trivial subgroup of Gc)G have exactly normal 2 non-trivial normal subgroups of given orderd)H ≠ φCorrect answer is option 'A'. 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 H be normal in G such that 0 (H) andare co-prime thena)H is only subgroup of G of 0(H)b)H is trivial subgroup of Gc)G have exactly normal 2 non-trivial normal subgroups of given orderd)H ≠ φCorrect answer is option 'A'. Can you explain this answer?.
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