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| + | Let ''a'' belong to a group ''G'' and let |''a''| be finite. Let <math>\phi_a</math> be the automorphism of ''G'' given by <math>\phi_a (x) = axa^{-1}</math>. Show that |<math>\phi_a</math>| divides |''a''|. Exhibit an element ''a'' from a group for which 1<|<math>\phi_a</math>|<|''a''|. | ||
Revision as of 15:46, 10 February 2009
Let a belong to a group G and let |a| be finite. Let $ \phi_a $ be the automorphism of G given by $ \phi_a (x) = axa^{-1} $. Show that |$ \phi_a $| divides |a|. Exhibit an element a from a group for which 1<|$ \phi_a $|<|a|.
