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zcahana
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Homework Statement
Let G be a finite group and N[tex]\triangleleft[/tex]G such that |N| = n, and gcd(n,[G:N]) = 1.
Proof that if x[tex]^{n} = e[/tex] then x[tex]\in[/tex]N.
Homework Equations
none.
The Attempt at a Solution
I defined |G| = m and and tried to find an integer which divides both n and m/n.
I went for some X which is not in N, for which X^n = e.
I defined o(X) = q and then q | n.
No luck showing that q | m/n.Any other ideas?Thanks ahead,
Zvi
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