Mathematics Exam > Mathematics Questions > Let G be a group of order 7 and Thenφ isa...
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Let G be a group of order 7 and 
Then φ is
Then φ is- a)not one-one
- b)not onto
- c)not a homomorphism
- d)one-one, onto and a homomorphism
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let G be a group of order 7 and Thenφ isa)not one-oneb)not ontoc)n...
G is a group of order 7 which is prime. So group will be cyclic and each element can generate it. Now, let x generate the group, then x1 = e.
Thus, φ is one-one and onto.
Also,
Thus, φ is one-one and onto.
Also,
Most Upvoted Answer
Let G be a group of order 7 and Thenφ isa)not one-oneb)not ontoc)n...
G is a group of order 7 which is prime. So group will be cyclic and each element can generate it. Now, let x generate the group, then x1 = e.
Thus, φ is one-one and onto.
Also,
Thus, φ is one-one and onto.
Also,
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Let G be a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. Can you explain this answer?
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Let G be a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. 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 a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. 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 a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. Can you explain this answer?.
Let G be a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. 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 a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. 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 a group of order 7 and Thenφ isa)not one-oneb)not ontoc)not a homomorphismd)one-one, onto and a homomorphismCorrect answer is option 'D'. Can you explain this answer?.
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