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Dhruv posted an Question
September 01, 2021 • 03:36 am 30 points
  • CSIR NET
  • Mathematical Sciences

Let r* denote the group of all nonzero real numbers under multi- plication. let rt denote the group of positive real numbers under multiplication. prove that r

Let R* denote the group of all nonzero real numbers under multi- plication. Let Rt denote the group of positive real numbers under multiplication. Prove that R is the internal direct product of R and the subgroup { 1, -1).

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    Kanika goswami 1

    obviously R* is internal direct product of R+ and subgroup {1,-1}....because when positive elements of R+ multiply with -1 then we will get negative real numbers....and when elements of R+ multiply with 1 then we will get positive real numbers.....i.e., we get whole R*......ok.

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