Prof Thekiso Seretlo, a mathematics professor at the North-West University (NWU), delivered a captivating inaugural lecture on 13 March 2024, at the NWU’s Mahikeng Campus.
The lecture, titled "The role of finite simple groups in Clifford-Fischer Theory: group generations, codes and designs", shed light on the significance of finite simple groups and their applications in contemporary mathematical theory.
At the core of Prof Seretlo's lecture was the role that finite simple groups played in the study of finite groups.
“The classification of the Finite Simple Group Theorem (CFSGT), a monumental theorem, was completed in 1984 after 150 years of collaborative effort within the mathematical community. More than 10 volumes of books have been written on this theorem, and it wasn't until 2004 that mathematicians agreed that everything about the classification of finite simple groups had been captured,” he said.
Highlighting the four classes of finite simple groups - cyclic groups of prime order, alternating groups, groups of lie type, and the 26 sporadic groups - Prof Seretlo emphasised the subsequent exploration of maximal subgroups and group extensions within these classifications.
Expounding upon the historical context of algebra and the fundamental concepts of groups and finite simple groups, Prof Seretlo delved into the application of the Clifford-Fischer Theory in constructing character tables for split extension groups. "We still employ this theory in analysing non-split extension," he added.
The lecture extended to the generation of simple groups and the principles underlying codes and designs, including the three methods employed to construct them from simple groups. Prof Seretlo underscored the practicality of his work by noting the inclusion of character tables computed using Clifford-Fischer matrices in the GAP library, facilitating access for mathematicians seeking to utilise them in their research.
"Group generations offer deeper insights into mathematical problem-solving, with applications extending to fields like physical chemistry," he added. Reflecting on the broader significance of mathematical inquiry, he referenced mathematician David Hilbert's famed 23 problems outlined in 1900, of which after 223 years only eight have been solved, emphasising their theoretical rather than practical nature.
"In essence, mathematics transcends mere application; it challenges the intellect and pushes the boundaries of human understanding," concluded Prof. Seretlo.
Prof David Modise, executive dean of the Faculty of Natural and Agricultural Sciences congratulated Prof Seretlo.
“Prof Seretlo has distinguished himself through his lifetime scholarly work and this lecture culminates in him being a full professor.
Congratulations once more, we know this is not the end of your contribution to scientific knowledge.
