COMPOSITION SERIES OF THE SOLVABLE ABELIAN FACTOR GROUP SOURCE OF EQUATION OF ALL POLYNOMIAL EQUATIONS

  • Bernard Alechenu Alechenu Oglekwu Ogbogwu
  • Babayo Muhammed Abdullahi
  • Daniel Eneojo Emmanuel
Keywords: Cauchy Sequence, Rouche Theorem, Class Equation, Aleph Naught

Abstract

This work penciled down the Composition Series of Factor Abelian Group over the source of all polynomial equations gleaned through  the nth roots of unity regular gons on a unit circle, a circle of radius one and centered at zero. To get the composition series, the third isomorphism theorem has to be passed through. But, the third isomorphism theorem itself gleaned via the first which is a deduction of the naturally existing canonical map. The solution of the source atom of the equation of all equation of polynomials are solvable by the intertwine of the Euler’s Formula and the De Moivre’s Theorem which after the inter-math, they become within the domain of complex analysis. For the source root of the equations, there is a recursive set of homomorphisms and ontoness of the mappings geneting the sequential terms in the composition series.

 

 

References

Anthony W K, Basic Real Analysis, Birkhauser Boston (2005). New York, USA,.

Burnside W (1897). Theory of Groups of Finite Order, Cambridge University Press, Cambridge, USA.

Buya S B (2017). The Bring-Jerrad Quintic Equation, Its Solvability by Factorization into Cubic and Quadratic Factors, Journal of Applied Science and Innovations, 1:16-21.

Christopher H. (2009) The Early Development of the Algebraic Theory of Semigroups, Archive for History of Exact Sciences, 63(5): 497-536.

Feit W, Thompson G J. (1963). Solvability of Groups of Odd Order, Pacific J. Math, 13 (3): 775 – 1029.

Gallian J A, (2013). Contemporary Abstract Algebra, Cengage Learning, India, 8th Edition,

Heinstein I N (1975). Topics in Algebra, John Wiley & Sons, 2nd Edition.

John J O’, Robertson E F (2017). Mac Tutor History of Mathematics, University of St Andrews, Scotland, UK.

Richard L R (2001). A History of Lagrange Theorem on Groups, Mathematics Magazine, 74(2): 99 - 108.

Seymour L , Murray R S, John J S, Dennis S. (2009). Complex Variables, McGraw-Hill Companies, United States of America, 2nd Edition.

Stanley B and Sankappanavar H P. (1981). A Course in Universal Algebra, Springer-Varlag, United States of America.

Vasistha A R, Vasistha A K. (2006). Modern Algebra (Abstract Algebra), Krishna Parakashan Media(P) Ltd, Meerut, Delhi.

Published
2021-07-17
How to Cite
Alechenu B., AbdullahiB. M., & EmmanuelD. E. (2021). COMPOSITION SERIES OF THE SOLVABLE ABELIAN FACTOR GROUP SOURCE OF EQUATION OF ALL POLYNOMIAL EQUATIONS. FUDMA JOURNAL OF SCIENCES, 5(2), 462 - 469. https://doi.org/10.33003/fjs-2021-0502-458