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Title: M-axial algebras related to 4-transposition groups
Author: Khasraw, Sanhan Muhammad Salih
ISNI:       0000 0004 5359 3970
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2015
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The main result of this thesis concerns the classification of 3-generated M-axial algebras A such that every 2-generated subalgebra of A is a Sakuma algebra of type NX, where N∈{2, 3, 4} and X∈{A, B, C}. This goal requires the classification of all groups $G$ which are quotients of the groups T\(^(\)\(^s\)\(^1\)\(^,\) \(^s\)\(^2\)\(^,\) \(^s\)\(^3\)\(^)\) = < x, y, z | x\(^2\), y\(^2\), z\(^2\), (xy)\(^s\)\(^1\), (xz)\(^s\)\(^2\), (yz)\(^s\)\(^3\) > for s\(_1\), s\(_2\), s\(_3\) ∈{3, 4} and the set of all conjugates of x, y and z satisfies the 4-transposition condition. We show that those groups are quotients of eight groups. We show which of these eight groups can be generated by Miyamoto involutions. This can be done by classifying all possible M-axial algebras for them. In addition, we discuss the embedding of Fisher spaces into a vector space over GF(2) in Chapter 3.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics