Vol. 6 No. 1 (2023): The Reality of Women in Science

• Jelten, B. Naphtali
  Department of Mathematics University of Jos, P.M.B. 2084, Plateau State, Nigeria.
  




• Audu, Buba
  Department of Mathematics and Statistics, American University of Nigeria Yola, Adamawa State Nigeria.
  




• Stephen Y. Kutchin
  Department of Mathematics University of Jos, P.M.B. 2084, Plateau State, Nigeria.
  




• Hassan, S. Bade
  Department of Mathematics Federal Collage of Education, Yola, Adamawa State, Nigeria.
  

Jelten N et al (2017) and (2019) in their work derived respectively rnschemes for the minimum and maximum number of the non - rnreducible (irreducible) representations of finite non- abelian 2 – rngroups. In this paper we derive using the Lagrange interpolation the rnLagrange polynomials for the minimum and maximum non - rnreducible representations of finite p -groups for even p. The minimum rnnumerical values we generated as part of our results were from the rnscheme rnas in theorem 1.18 of this paper while the maximum rnvalues generated as parr of our results were obtained from the scheme rna rnas in theorem 1.19 of our paper. Here we express properties of rnabstract structures in numerical forms where we write |G| as card(G) rnand |C| as min rep(G) and max (G) for the minimum and maximum rnrespectively. With this we derive entirely new results creating a rnrelationship between the abstract part of pure mathematics and the rnnumerical part of applied mathematics. Surprisingly our results agree rnwith those of Jelten, N et al. The schemes we obtain have fantastic rnproperties as they can be used to generate minimum and maximum rnnon- reducible representations of other groups by inserting integral rnvalues. This is a characteristic of numerical analysis. In our work we rnemploy the results of Jelten, N. et al (2017) and (2019) and Lagrange rninterpolation polynomial as the main tools to derive our results.

Keywords: centre, abelian, group, Lagrange`s polynomial, representation