Sheila Oates Williams

Sheila Oates Williams (born 1939[1], also published as Sheila Oates and Sheila Oates Macdonald)[2] is a British and Australian mathematician specializing in abstract algebra. She is the namesake of the Oates–Powell theorem in group theory, and a winner of the B. H. Neumann Award.

Not to be confused with Sheila Williams.

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 in St Hugh's College, Oxford, with Ida Busbridge as her tutor, and continued at Oxford as a doctoral student of Graham Higman.[3] She completed her doctorate (D.Phil.) in 1963.[4]

She became a lecturer and fellow at St Hilda's College, Oxford, before moving to Australia in 1965. In 1966, she took a position as senior lecturer at the University of Newcastle and later moved again to the University of Queensland, as reader. She retired in 1997.[3]

Contributions

As a student at Oxford, with Martin B. Powell, another student of Higman,[3] she proved the Oates–Powell theorem. This is an analogue for group theory of Hilbert's basis theorem,[5] 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.[6][7]

As well as for her research, Williams is known for her work setting Australian mathematics competitions, including the International Mathematical Olympiad in 1988 and the Australian Mathematics Competition. She also participated several times in the Australian edition of the Mastermind television quiz show.[3]

Recognition

Williams was a 2002 recipient of the B. H. Neumann Award for Excellence in Mathematics Enrichment of the Australian Maths Trust.[3][8]

References
  1. Birth year from Library of Congress catalog entry, retrieved 2021-05-29
  2. 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)
  3. Taylor, Peter, 2002 B. H. Neumann Award Recipients, Australian Maths Trust, retrieved 2021-05-29
  4. Sheila Oates Williams at the Mathematics Genealogy Project
  5. 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
  6. Neumann, Hanna (1967), "5.2 The theorem of Oates and Powell", Varieties of Groups, Springer, pp. 151–161, doi:10.1007/978-3-642-88599-0, MR 0215899
  7. Oates, Sheila; Powell, M. B. (1964), "Identical relations in finite groups", Journal of Algebra, 1: 11–39, doi:10.1016/0021-8693(64)90004-3, MR 0161904
  8. "B. H. Neumann Awards Given" (PDF), Mathematics People, Notices of the American Mathematical Society, 49 (10): 1270, November 2002
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