Normalizers and centralizers of subgroups in non-Abelian groups of small order

Abstract

By applying the computer program, which is created by authors, we obtain the exact representation of normalizers and centralizers of all nontrivial subgroups in non-Abelian groups G under the condition |G|20. All results are represented either in terms of concrete realization of the corresponding group or in terms of it's generators. We consider the application of our program to the verification of T-normal condition.

Keywords

• normilizer
• centralizer
• finite group
• non-Abelian group
• T-normal group