1. The absolute Galois group is well-defined up to inner automorphism . 2. As a subgroup, it is always isomorphic to the inner automorphism group,. 3. For the automorphism group is Z 2, with trivial inner automorphism group and outer automorphism group Z 2. 4. In particular, every automorphism of a central simple " k "-algebra is an inner automorphism . 5. The inner automorphism group is isomorphic to A _ 4, and the full automorphism group is isomorphic to S _ 4. 6. I love the example given in Inner automorphism : " take off shoes, take off socks, put on shoes ". 7. Every non-inner automorphism yields a non-trivial element of, but different non-inner automorphisms may yield the same element of. 8. *PM : groups with abelian inner automorphism group, id = 9799 new !-- WP guess : groups with abelian inner automorphism group-- Status: 9. *PM : groups with abelian inner automorphism group, id = 9799 new !-- WP guess : groups with abelian inner automorphism group-- Status: 10. :Perhaps reading Inner automorphism # The inner and outer automorphism groups will give you a hint .-- Talk 15 : 52, 13 June 2007 ( UTC)
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