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Symmetrically Generated Groups, Benny Nguyen
Symmetrically Generated Groups, Benny Nguyen
Theses Digitization Project
This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt
Theses Digitization Project
Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.