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The structure of EAP-groups and self-autopermutable subgroups.

Shima Housieni1, Mohammad Reza Rajabzadeh Moghaddam2

  • 1Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad 9187147578, Iran.

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|January 10, 2015
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Summary

This study explores autopermutable subgroups within groups, defining EAP-groups. It determines the structure of finite EAP-groups with a center of index 4 and proves self-autopermutability is equivalent to characteristic properties in nilpotent groups.

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Area of Science:

  • Group Theory
  • Abstract Algebra
  • Computational Mathematics

Background:

  • Introduces autopermutable subgroups and EAP-groups.
  • Relates concepts to conjugate-permutability and ECP-groups.
  • Highlights existing research by Foguel, Li, Meng, Xu, and Zhang.

Purpose of the Study:

  • Determine the structure of finite EAP-groups with a center of index 4.
  • Investigate the relationship between self-autopermutability and characteristic properties in nilpotent groups.

Main Methods:

  • Utilizes abstract algebraic techniques.
  • Applies group-theoretic properties and automorphism concepts.
  • Focuses on structural analysis of finite groups.

Main Results:

  • Characterizes finite EAP-groups where the group's center has index 4.
  • Establishes the equivalence of self-autopermutability and characteristic properties for nilpotent groups.

Conclusions:

  • Provides structural insights into a specific class of EAP-groups.
  • Demonstrates a key equivalence for nilpotent groups, simplifying characterizations.