Michael Nsikan John

Michael Nsikan John
Akwa Ibom State University · Department of Mathematics

PhD Mathematics - (Pure Mathematics/Algebra)

About

33
Publications
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194
Citations
Introduction
Michael NsikanJohn holds a PhD in Pure Mathematics(Algebra) from Akwa Ibom State University. Michael does research in Algebra; Group theory, Computational Group theory, Semigroup, Transformation Groups,Transformation Semigroup, Algebraic Cryptography, Combinatorics, Blockchain technology and development, Financial Mathematics. Their current project is 'Group Theory in Lattice-Based Cryptography'.

Publications

Publications (33)
Article
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In this paper, we propose an enhanced algorithmic approach for resolving the Modular Isomorphism Problem (MIP) for groups of small orders. Building upon Eick's algorithm, our improvement obviates the need for computing the full augmentation ideal, thereby significantly enhancing computational efficiency. Through our computations, we provide affirma...
Article
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This paper reviews the work of M.I. Sampson et. Al (2023) [7], and delves into the intricate relationship between minimal generating sets and independence in semigroups by examining the comparability of elements induced by orderings on the semigroup. It demonstrates that the existence of a minimal generating set implies independence, and conversely...
Article
This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups 𝐺. By delving into three distinct forms of full transitivity within the endomorphism ring of 𝐺, specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphi...
Article
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This research delves into the examination of weak solutions for boundary value problems associated with nonlinear partial differential equations. Utilizing the variational method, we explore the conditions necessary and sufficient for the existence and uniqueness of these weak solutions. Furthermore, we provide practical demonstrations by solving s...
Article
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This research delves into the intricate structure of conjugacy classes within finitely generated groups possessing small cancellation properties. Focusing on groups derived from the free group on two generators (2) through small cancellation theory, the study explores the interplay between small cancellation conditions, conjugacy classes, and their...
Article
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This paper investigates the finite groups for which any two characters in the set of irreducible complex characters () are Galois conjugate. Specifically, we classify such groups and establish a key result: they are solvable with Fitting height 2. The analysis involves intricate considerations of irreducible complex characters and their Galois conj...
Article
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This research explores the interplay between residually nilpotent groups and , focusing on their relationship through the lens of para-conditions and the Hirsch length. We establish criteria for to be para-concerning monomorphisms inducing isomorphisms between corresponding lower central quotients of and. Specifically, we investigate these conditio...
Article
Full-text available
This research addresses the problem posed by Chekhlov and Danchev (2015) regarding variations of Kaplansky's full transitivity in primary abelian groups. By delving into three distinct forms of full transitivity within the endomorphism ring of , specifically focusing on subgroups, subrings, and unitary subrings generated by commutator endomorphisms...
Article
Full-text available
This paper introduces a robust and mathematically rigorous lattice-based cryptographic scheme to enhance the security of blockchain networks, with a focus on financial systems. With the advent of quantum computing, traditional cryptographic systems like RSA and ECC face vulnerabilities that lattice-based schemes can effectively mitigate. The propos...
Article
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This paper investigates the algebraic properties of the enveloping semigroupE of a transformation group (X,T,μ) with a compact Hausdorff phase space X. The transition group G is considered as a group of homeomorphisms on X, and E is defined as the closure of G in X×X. The main focus is on establishing a connection between the proximal equivalence r...
Article
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This research delves into the multifaceted applications of transformation semigroups, leveraging insights from algebraic cryptography, group theory, blockchain technology, and computational mathematics. Through a comprehensive exploration, we unveil novel cryptographic protocols, enhance blockchain consensus algorithms, develop efficient computatio...
Article
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This paper explores the construction and properties of B-Algebras derived from Modulo Integer Groups, specifically focusing on the set of residue classes modulo , denoted as .The algebraic structure is built by incorporating modulo addition and a binary operation, leading to a B-Algebra over. The paper also establishes the framework for investigati...
Article
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In this paper, we establish a significant result concerning solvable groups G and their Sylow p-subgroups. We demonstrate that if the codegree cod(χ) is a p-power for every nonlinear, monomial, monolithic character χ in either Irr(G) or IBr(G), then the Sylow p-subgroup P is normal in G. This provides a deeper understanding of the interplay between...
Article
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This research investigates finite groups in the context of partitions of prime numbers, denoted as. Specifically, we explore the characteristics of groups where every-subnormal subgroup is modular. The study aims to provide a comprehensive understanding of the structural properties that contribute to modularity within finite groups, shedding light...
Article
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This research investigates the relationships between finite linear groups, nilpotent normal subgroups, and the concept of Hall classes. We explore the theorem established by Philip Hall, which asserts conditions under which a group is nilpotent. Contrary to existing examples presented in the literature, we delve into specific subclasses within the...
Article
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This paper explores finite groups G with a focus on those that are strongly base-two and possess a trivial Frattini subgroup. The concept of base size, denoted by b(G, H), for the action of G on core-free subgroups H, plays a crucial role. The paper investigates the number of conjugacy classes of core-free subgroups with base size exceeding 3, deno...
Article
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RSA encryption is a widely employed cryptographic system based on the principles of number theory. Number theory is the branch of pure mathematics that studies positive whole numbers, called natural numbers and integers. Number theory seeks to discover relationships existing between numbers. decryption of information. By encrypting information, dat...
Article
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Cryptographic systems play a pivotal role in securing sensitive information in fundamental component of classical cryptography, involve the rearrangement of characters in a message to achieve confidentiality. This paper explores the principles and applications of permutation ciphers in cryptogr encryption. The study delves into the historical conte...
Article
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The use of Mathematic in cryptography can result a safe encryption scheme. Lattices have emerged as a powerful mathematical tool in the field of cryptography, offering a diverse set of applications ranging from encryption to secure multi-party computation. This research paper provides a comprehensive review of the role of lattices in cryptography,...
Article
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Elliptic Curve Cryptography (ECC) has gained widespread adoption in the field of cryptography due to its efficiency and security properties. Symmetric bilinear pairings on elliptic curves have emerged as a powerful tool in cryptographic protocols, enabling advanced constructions and functionalities. This paper explores the intersection of symmetric...
Article
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Elliptic-curve group cryptography (ECC) has been widely recognized as a robust and efficient cryptographic system in the classical era. However, with the emergence of quantum computing, traditional public key cryptosystems are at risk of being broken, which has prompted the exploration of alternative cryptographic methods. This research paper explo...
Article
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This research presents a novel key agreement protocol leveraging the rich mathematical structure of conjugacy classes within groups. We propose a key agreement protocol based on finitely generated group drawing inspiration from algebraic cryptography, specifically group theory, to establish a secure and efficient means of key exchange, through the...
Article
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This paper provides a thorough exploration of the applications of nilpotent groups for some n ≥ 1 in cryptography, focusing on their unique algebraic properties and their role in designing secure cryptographic systems. Through an in-depth analysis of cryptographic protocols utilizing nilpotent groups, this paper contributes to a deeper understandin...
Article
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This paper provides an overview of the significant role of computational group theory in cryptography. Group theory plays a crucial role in various cryptographic applications, such as key exchange, encryption, and digital signatures. This paper examines the fundamental concepts, algorithms, and applications of computational group theory in cryptogr...
Article
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Cube-lattice-based cryptography stands as a pivotal development in the intersection of mathematics and cybersecurity. Its quantum resistance, versatility, and cryptographic capabilities position it as a crucial component in the ongoing efforts to secure data communication and protect privacy in an increasingly digital world. This paper seeks to adv...
Experiment Findings
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In 2020, Nigeria experienced lockdown and it affected the school systems especially Colleges of Education. This resulted in a new challenge for students and lecturers; lectures were moved from the lecture halls to students' homes. Therefore, lecturers of mathematics had to set rules, implement procedures and make didactical-methodical decisions reg...
Article
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This study investigates the number of homomorphisms from the quaternion group into various finite groups. Quaternion groups, denoted as Q8, possess unique algebraic properties that make them intriguing subjects for group theory inquiries. The research explores the enumeration of homomorphisms from Q8into specific finite groups, providing insights i...
Article
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The study investigates the role of group actions on fuzzy R-subgroups within the context of near-rings. Utilizing the notion of fuzzy sets, this research explores the interaction between groups and certain subsets of near-rings, known as R-subgroups. Through the lens of group actions, a deeper understanding of the structural properties and dynamics...
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This research delves into the co-maximal subgroup graph of the integer modulo group,. Investigating the structural properties of this graph provides insights into the relationships among subgroups of. We explore the connectivity, patterns, and specific cases, offering a comprehensive analysis of this algebraic structure. Through a combination of gr...
Article
Full-text available
Elliptic Curve Cryptography (ECC) has gained widespread adoption in the field of cryptography due to its efficiency and security properties. Symmetric bilinear pairings on elliptic curves have emerged as a powerful tool in cryptographic protocols, enabling advanced constructions and functionalities. This paper explores the intersection of symmetric...
Article
Full-text available
Group theory plays a fundamental role in lattice-based cryptography, providing a rich mathematical framework for the design and analysis of cryptographic protocols. This paper explores the application of group theory concepts within lattice-based cryptographic systems, focusing on the algebraic structures formed by lattices and their subgroups. The...
Article
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In this paper, we establish characterization theorems akin to C. Reid's work on just infinite profinite groups, focusing on just infinite profinite residually solvable Lie algebras. Specifically, we prove that a profinite residually solvable Lie algebra attains just infiniteness if and only if its obliquity subalgebra exhibits finite codimension wi...
Thesis
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This study is all about the nonlinear heat transfer equation's computational analysis. In this study, we demonstrate how to perform a thin plate heat transfer analysis. The plate is square and the bottom edge temperature is fixed. No heat is transferred (i.e. they are insulated) from the other three edges. Heat is transferred by convection and radi...

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