## Journal of Applied Mathematics and Computation

 ISSN Print: 2576-0645 Downloads: 101739 Total View: 1490384 Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ Email: jamc@hillpublisher.com

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Article http://dx.doi.org/10.26855/jamc.2024.06.003

# On Expectation of Generating Certain Finite Nilpotent Groups

Khaled Alajmi

Department of Mathematics, Public Authority for Applied Education and Training, Ardiyah, Kuwait.

*Corresponding author:Khaled Alajmi

Published: July 12,2024

## Abstract

Let G be a finite group. Define E(G) to be the expected number of elements of G which have to be drawn at random with replacement from G before a set of generators is found. The purpose of this paper is to compute E(G) for certain nilpotent groups. This paper is divided into six sections. The first section is an introduction. In the second section we present the definition λn (G) the probability that n elements drawn at random, with replacement from a finite group G generate G, and the definition E(G) the expectation of the group G, that is the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators is found. In the third section we present some preliminaries and earlier results e.g if G is a group and Φ(G) is its Frattini subgroup. Then, λn (G)=λn (G/Φ(G)). In section four, we computed E(G) for certain nilpotent groups such as and  In section five, we computed E(G) for a non-trivial example. The last section is a conclusion.

## References

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## How to cite this paper

On Expectation of Generating Certain Finite Nilpotent Groups

How to cite this paper: Khaled Alajmi. (2024) On Expectation of Generating Certain Finite Nilpotent GroupsJournal of Applied Mathematics and Computation8(2), 113-119.

DOI: http://dx.doi.org/10.26855/jamc.2024.06.003