Sheila Oates Williams (born 1939[1] – 12 August 2024[2], also published as Sheila Oates and Sheila Oates Macdonald)[3] was a British and Australian mathematician specializing in abstract algebra. She was the namesake of the Oates–Powell theorem in group theory, and a winner of the B. H. Neumann Award.
Education and career
Sheila Oates was originally from Cornwall, where her father was a primary school headmaster in Tintagel. She was educated at Sir James Smith's Grammar School, and inspired to become a mathematician by a teacher there, Alfred Hooper. She read mathematics at St Hugh's College, Oxford, with Ida Busbridge as her tutor, and continued at Oxford as a doctoral student of Graham Higman.[4] She completed her doctorate (D.Phil.) in 1963.[5]
As a student at Oxford, with Martin B. Powell, another student of Higman,[4] she proved the Oates–Powell theorem. This is an analogue for group theory of Hilbert's basis theorem,[6] and states that all finite groups have a finite system of axioms from which can be derived all equations that are true of the group. That is, every finite group is finitely based.[7][8]
^Neumann, Bernhard (1999), "Professor Cheryl Praeger, mathematician", Interviews with Australian scientists, Australian Academy of Science, retrieved 2021-05-29, Sheila started as Sheila Oates, became Sheila Macdonald and now is Sheila Williams, which is a very good case against a woman changing her professional name on marriage (her first marriage was to Neil Macdonald)
^Chandler, Bruce; Magnus, Wilhelm (1982), "Varieties of groups", The History of Combinatorial Group Theory, Studies in the History of Mathematics and Physical Sciences, vol. 9, Springer, pp. 157–161, doi:10.1007/978-1-4613-9487-7_19, ISBN978-1-4613-9489-1