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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by F. de Giovanni.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11587-010-0085-6