/sci/ - Science & Math

>>11709820
No, you reindex.
You seem to understand extremely explicit computations, so I'll just give you one.
[math]b = c^{-1} (n+1)[/math], just to fix notation.
Then, [math]( \sigma ')^{-1} \circ [ \sigma \circ c] = (b, n+1)[/math].
So, because all of those three on the left belong in [math]H[/math] , so does [math](b, n+1)[/math].
Then, [math](1, b)^{-1} (b, n+1) (1, b) = (1, n+1)[/math], by the formula here >>11709812 , and then [math](1, n+1) \in H [/math] .
The formula is proved by simple computation. In other words, you check it manually for [math]a[/math], [math]b[/math] and [math]c[/math], i.e. [math][(a, c)(a, b)(a, c)](a)= [(a, c)(a, b)](c) = (a, c) (c) = a[/math].

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