Normal Automorphisms of Free Burnside Groups of Period 3

Authors

  • Varujan Atabekyan Head of Chair Algebra and Geometry, Yerevan State University
  • H.T. Aslanyan Russian-Armenian University, 123 Hovsep Emin str. 0051 Yerevan, Armenia
  • A. E. Grigoryan Russian-Armenian University, 123 Hovsep Emin str. 0051 Yerevan, Armenia

Keywords:

normal automorphism, inner automorphism, periodic group, free Burnside group, free group

Abstract

If any normal subgroup of a group $G$ is $\phi$-invariant for some automorphism $\phi$ of $G$, then $\phi$ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group $B(m,3)$ of period 3 is inner for all rank $m\ge3$.

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Published

2017-12-26

Issue

Vol. 9 No. 2 (2017)

Section

Articles

How to Cite

[1]
V. Atabekyan, H. Aslanyan, and A. E. Grigoryan, “Normal Automorphisms of Free Burnside Groups of Period 3”, Armen.J.Math., vol. 9, no. 2, pp. 60–67, Dec. 2017, Accessed: Jan. 26, 2025. [Online]. Available: https://armjmath.sci.am/index.php/ajm/article/view/157