ScholarLens Back to search
2013•International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statisticsOpen access

The probability that an element of a group fixes a set and the group act on set by conjugation

S. M. S. Omer, Nor Haniza Sarmin, Ahmad Erfanian, Kayvan Moradipour

Open full text 15 citations

Abstract

The commutativity degree is the probability that two random elements commute in G, and denoted as P(G). The main purposes of this paper is to find the probability of an element of a group G fixes a set X. The set X is in the form (a; b), where a and b are commuting element in G of size 2 and the group G acts on the set of all subset of X by conjugation. A new definition of this probability is introduced. Among other results, some upper bounds for P(G) are provided.

About this research paper

What this paper is about

The commutativity degree is the probability that two random elements commute in G, and denoted as P(G). The main purposes of this paper is to find the probability of an element of a group G fixes a set X. The set X is in the form (a; b), where a and b are commuting element in G of size 2 and the group G acts on the set of all subset of X by conjugation. A new definition of this probability is introduced. Among other results, some upper bounds for P(G) are provided.

Why it matters

OpenAlex reports 15 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

The commutativity degree is the probability that two random elements commute in G, and denoted as P(G). The main purposes of this paper is to find the probability of an element of a group G fixes a set X. The set X is in the form (a; b), where a and b are commuting element in G of size 2 and the group G acts on the set of all subset of X by conjugation. A new definition of this probability is introduced. Among other results, some upper bounds for P(G) are provided.

Key concepts: Element (criminal law), Group (periodic table), Set (abstract data type), Commutative property, Mathematics, Combinatorics, Maximal element, Discrete mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The probability that an element of a group fixes a set and the group act on set by conjugation — Research Paper | ScholarLens