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Vaishnavi Mishra posted an Question
January 08, 2022 • 15:20 pm
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Ab realme shot on realme 8 5g 2022/01/08 09:49
how to approach thitype of problem........................
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Pranshu
yes if grp is abelian then we can say that group of order n is isomorphic when gcd of n and order of given mapping are relatively prime with each other
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Anonymous User
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we know Group of prime order is cyclic therefore G is cyclic and x⁷=e f(x)=x⁴ f(x²)=x⁸=x f(x³)=x¹²=x⁵ f(x⁴)=x¹⁶=x² f(x⁵)=x²⁰=x⁶ f(x⁶)=x²⁴=x³ f(x⁷)=x²⁸=x⁷ so one one onto homomorphism
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sir how f(x)=x⁴ is onto homo. this can't be bcz we read that a trivial mapping is not to be countable in onto homo.
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sir ye process nhi samjh aa rha hai kya meaning hai ?
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prime order ka group cyclic hota hai agar two same order ke cyclic group le to mapping one one onto homomorphism hoti hai
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Pranshu
you have to remember gcd (7,4)=1 so this is one one onto homo.=isomorphic