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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.