Inner Automorphisms of Non-commutative Analogues of the Additive Group of Rational Numbers
نویسنده
چکیده
Introduction. The inner automorphism of an element g of a group G is denoted by ig and is given by the formula xig = gxg−1 for all x ∈ G. The mapping π : G→Aut(G), taking each g∈G to the inner automorphism ig, is a homomorphism, Ker(π) = Z(G) and Im(π) = Inn(G). It is easy to check that the automorphism group Aut(G) of a group G with trivial center also is a group with trivial center. Therefore, in this case, we obtain a sequence of embeddings G→ Aut(G)→ Aut(Aut(G)) = Aut2(G)→ Aut3(G)→ ... (1)
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