Prof Thekiso Seretlo

The lecture first looked at the Persian origins of algebra from Mohamed Kawarizmi in the 9th century and the development into abstract or modern algebra in the 19th century. The classification of finite simple groups, a theorem that took over 150 years to develop, was eventually finished in 1984. Finite simple groups can be classified into four types, namely cyclic groups of prime order, alternating groups of a degree greater than 4, groups of Lie type, and the 26 sporadic groups. The largest sporadic group is the Monster, of the order of about 8 x 1053 . From the finite simple groups there was an investigation into maximal subgroups of finite simple groups. Some of these maximal subgroups were group extensions, and Bernd Fischer developed a method called Clifford Fischer to compute the character tables of these groups. These were of split and non-split extensions, where the base was an elementary abelian group. Lastly, we looked at split extensions, where the base was non-abelian. A definition of three group generations and methods to compute them was given, and lastly the definitions of codes and designs and three methods to compute them was given.