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On the decidability of the integrability of finite groups

Sathasivam Kalithasan, Viji Z. Thomas

Abstract

An integral of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. In this paper, we prove that the integrability of a finite group is a decidable problem.

On the decidability of the integrability of finite groups

Abstract

An integral of a group is a group whose commutator subgroup is isomorphic to . In this paper, we prove that the integrability of a finite group is a decidable problem.
Paper Structure (3 sections, 7 theorems, 17 equations)

This paper contains 3 sections, 7 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Preliminary results
  3. Bounds on the size of the integral of group

Key Result

Theorem 1

Let $G$ be a finite group. If $G$ is integrable, then $G$ has an integral $Q$ with

Theorems & Definitions (11)

  • Theorem
  • Corollary
  • Theorem : ACC2024, Theorem 2.1
  • Example
  • Theorem 2.1: ACC2024, Theorem 2.1
  • Definition 2.2
  • Lemma 3.1
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • ...and 1 more