Abstract
Let G be a group, Aut(G) and L(G) denote the full automorphisms group and absolute centre of G, respectively. The automorphism \({\alpha\in Aut(G)}\) is called autocentral if \({g^{-1}\alpha(g)\in L(G)}\), for all \({g\in G}\). In the present paper, we investigate the properties of such automorphisms.
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References
Adney J.E., Yen T.: Automorphisms of a p-group. Illinois J. Math. 90, 137–143 (1965)
Deaconescu M., Walls G.L.: Cyclic groups as autocommutator groups. Commun. Algebra 35, 215–219 (2007)
Franciosi S., Giovanni F.D., Newell M.L.: On central automorphisms of infinite groups. Commun. Algebra 22(7), 2559–2578 (1994)
Hegarty P.V.: The absolute centre of a group. J. Algebra 169, 929–935 (1994)
Jamali A., Mousavi H.: On the central automorphism groups of finite p-groups. Algebra Colloquium 9(1), 7–14 (2002)
Moghaddam, M.R.R., Parvaneh, F., Naghshineh, M.: On the lower autocentral series of abelian groups. Bull. Korean Math. Soc (to appear)
Robinson D.J.S.: A Course in the Theory of Groups. 2nd edn. Springer, New York (1995)
Sapiro, A.P.: The absolute centre of an abelian group. Trady Naucn Ob ed. Prepodav. Fiz. Mat. Fak. Ped. Inst. Dal n. Vostok 7 (1996)
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Communicated by F. de Giovanni.
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Moghaddam, M.R.R., Safa, H. Some properties of autocentral automorphisms of a group. Ricerche mat. 59, 257–264 (2010). https://doi.org/10.1007/s11587-010-0085-6
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DOI: https://doi.org/10.1007/s11587-010-0085-6