mathematics

Graham Higman

Graham Higman is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Graham Higman rather than just read about it. In short: Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory. Biography Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning a scholarship to Balliol College, Oxford.

Key takeaways

Graham Higman belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Graham Higman to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Graham Higman from memory before moving on to harder problems.

Reference excerpt

Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory.

Biography Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning a scholarship to Balliol College, Oxford. In 1939 he co-founded The Invariant Society, the student mathematics society, and earned his DPhil from the University of Oxford in 1941. His thesis, The units of group-rings, was written under the direction of J. H. C. Whitehead. From 1960 to 1984 he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. Higman was awarded the Senior Berwick Prize in 1962 and the De Morgan Medal of the London Mathematical Society in 1974. He was the founder of the Journal of Algebra and its editor from 1964 to 1984. Higman had 51 D.Phil. students, including Jonathan Lazare Alperin, Rosemary A. Bailey, Marston Conder, John Mackintosh Howie, and Peter M. Neumann. He was also a local preacher in the Oxford Circuit of the Methodist Church. During the Second World War he was a conscientious objector, working at the Meteorological Office in Northern Ireland and Gibraltar. He died in Oxford.

Publications Higman, Graham (1940). "The units of group-rings". Proceedings of the London Mathematical Society. (2). 46: 231–248. doi:10.1112/plms/s2-46.1.231. Feit, Walter; Higman, Graham (1964). "The nonexistence of certain generalized polygons". Journal of Algebra. 1 (2): 114–131. doi:10.1016/0021-8693(64)90028-6. Graham Higman (1966) Odd characterisations of finite simple groups, U. of Michigan Press *Graham Higman (1974), Finitely presented infinite simple groups, Notes on Pure Mathematics, vol. 8, Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra, ISBN 978-0-7081-0300-5, MR 0376874 Graham Higman and Elizabeth Scott (1988), Existentially closed groups, LMS Monographs, Clarendon Press, Oxford

See also Higman–Sims group, named after Donald G. Higman, but studied also by Graham Higman. Higman's embedding theorem Feit-Higman theorem Higman group Higman's lemma HNN extension Hall–Higman theorem

Notes

References Interview on YouTube Death notice, Oxford University Gazette, 17 April 2008 Archived 24 April 2008 at the Wayback Machine

External links O'Connor, John J.; Robertson, Edmund F., "Graham Higman", MacTutor History of Mathematics Archive, University of St Andrews Graham Higman at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Graham Higman

Start with the simplest possible case. Write down what Graham Higman claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Graham Higman before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Graham Higman ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Graham Higman

In research: Graham Higman appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Graham Higman in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Graham Higman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1917 births, 2008 deaths, 20th-century English mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Graham Higman outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Graham Higman” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Graham Higman in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Graham Higman means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Graham Higman out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Graham Higman in simple terms?

Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory. Biography Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning a scholarship to Balliol College, Oxford.

Why does Graham Higman matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Graham Higman?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Graham Higman.