Normal Automorphisms of Free Burnside Groups of Period 3

  • 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 $m\ge3$.

Published
2017-12-26
How to Cite
Atabekyan, V., Aslanyan, H., & Grigoryan, A. E. (2017). Normal Automorphisms of Free Burnside Groups of Period 3. Armenian Journal of Mathematics, 9(2), 60-67. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/157
Section
Articles