Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A survey on power maps in groups

Saikat Panja, Anupam Singh

Abstract

The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $viz.$ the map $x\mapsto x^M$ for a group $G$, and an integer $M\geq 2$. Here, we accumulate various results on the subject and pose some questions.

A survey on power maps in groups

Abstract

The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; the map for a group , and an integer . Here, we accumulate various results on the subject and pose some questions.

Paper Structure

This paper contains 3 sections, 5 theorems, 16 equations, 1 table.

Table of Contents

  1. Introduction
  2. Power maps in finite groups
  3. Power maps: Beyond finite groups

Key Result

Lemma 2.1

The $M$-th root in the following matrix groups are given as follows:

Theorems & Definitions (11)

  • Lemma 2.1
  • Definition 2.2
  • Example 2.3
  • Example 2.4
  • Lemma 2.5
  • Example 2.6
  • Theorem 2.7
  • Theorem 2.8
  • Example 2.9
  • Theorem 3.1
  • ...and 1 more