ON THE GROUPS OF THE INFINITELY GENERATED FREE ABELIAN GROUPS AUTOMORPHISMS
Abstract
Let A be an infinitely generated free abelian group. The paper shows that all automorphisms of the group Aut(A) are inner.
About the Author
V. A. Tolstykh
Istanbul Arel University
Turkey
Vladimir A. Tolstykh – Doctor of Physics and Mathematics, Professor at the Department of Mathematics and Informatics
Turkey
Vladimir A. Tolstykh – Doctor of Physics and Mathematics, Professor at the Department of Mathematics and Informatics
References
1. Dyer J., Formanek E. The automorphism group of a free group is complete // J. London Math. Soc. 11 (1975). Р. 181 – 190.
2. Dyer J., Formanek E. Automorphism sequences of free nilpotent group of class two // Math. Proc. Camb. Phil. Soc. 79 (1976). P. 271 – 279.
3. Dyer J., Formanek E. Characteristic subgroups and complete automorphism groups // Amer. J. Math. 99 (1977). P. 713 – 753.
4. Hua L. K., Reiner I. Automorphisms of the unimodular group // Trans. Amer. Math. Soc. 71 (1951). Р. 331 – 348.
5. O’Meara O. A general isomorphism theory for linear groups // J. Algebra. 44 (1977). Р. 93 – 142.
6. Tolstykh V. The automorphism tower of a free group // J. London Math. Soc. 61 (2000). P. 423 – 440.
7. Tolstykh V. Infinitely generated free nilpotent groups: completeness of the automorphism groups // Math. Proc. Camb. Phil. Soc. 147 (2009). P. 541 – 566.
8. Tolstykh V. On the Bergman property for the automorphism groups of relatively free groups // J. London Math. Soc. (2) 73 (2006). P. 669 – 680.
9. Tolstykh V. Small conjugacy classes in the automorphism groups of relatively free groups // J. Pure Appl. Algebra. 215 (2011). P. 2086 – 2098.
Review
For citations:
Tolstykh V.A. ON THE GROUPS OF THE INFINITELY GENERATED FREE ABELIAN GROUPS AUTOMORPHISMS. SibScript. 2015;1(2-1):46-47. (In Russ.)
Views:
407
Email this article 