Mathematics Homework Solutions
#107391
Normal Subgroups
Let G be a finite group, let N be a normal subgroup of G, and let x be an
element of G. Show that if the order of x in G is relatively prime to
|G|/|N|, then x is an element of N.
We know that xNx^(-1) is identical to N when N is normal, for any x.
Also we know that |G|/|N| is a factor of (or divides) |G|.
How to show x in G is also in N?
This is a proof regarding a normal subgroup.
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