Let p be prime. In any finite group, prove that the number of elements satisfying xp-...

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Let p be prime. In any finite group, prove that the number of elements satisfying xp- id. is a multiple of p-1. (Note, our author uses e for the identity instead of id. or 1.) The fact that p is prime is important. For example, there are not 7 non-identity elements of (Z/5ZX=U (5), ) to satisfy x8= 1. Make sure your proof accounts for this. Let p be prime. In any finite group, prove that the number of elements satisfying xp- id. is a multiple of p-1. (Note, our author uses e for the identity instead of id. or 1.) The fact that p is prime is important. For example, there are not 7 non-identity elements of (Z/5ZX=U (5), ) to satisfy x8= 1. Make sure your proof accounts for this.

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Let p is a prime it is given we have to prove that for any finite group xp1i... View the full answer