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Vaishnavi mishra Asked a Question
January 8, 2022 9:50 ampts 30 pts
how to approach thitype of problem........................
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  • Pranshu
    you have to remember gcd (7,4)=1 so this is one one onto homo.=isomorphic
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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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  • Navdeep goyal 1 thankyou
    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 homom...
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    Pranshu
    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.