(no subject)
Let [;R^*;] be the set of all real numbers, less the number 0, treated as a group under multiplication. Let [;(R^*)^+;] be the set of all positive real numbers under multiplication.
Clearly, [;(R^*)^+ \subset R^*;]. Now, firstly, we see that [;[R^*:(R^*)^+];] = 2. So it has index 2. As well, note that [;(R^*)^+ \lhd* R^*;] (Ie The first is normal in the second) so the factor group is defined. What is [;R^*/(R^*)^+;]?
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Clearly, [;(R^*)^+ \subset R^*;]. Now, firstly, we see that [;[R^*:(R^*)^+];] = 2. So it has index 2. As well, note that [;(R^*)^+ \lhd* R^*;] (Ie The first is normal in the second) so the factor group is defined. What is [;R^*/(R^*)^+;]?
(Note; Im using This addon for firefox to display latex characters properly.)