mathematics

Michael O'Nan

Michael O'Nan 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 Michael O'Nan rather than just read about it. In short: Michael Ernest O'Nan (August 9, 1943, Fort Knox, Kentucky – July 31, 2017, Princeton, New Jersey) was an American mathematician, specializing in group theory. O'Nan received his PhD in 1970 from Princeton University under Daniel Gorenstein with thesis A Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field.

Key takeaways

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

Reference excerpt

Michael Ernest O'Nan (August 9, 1943, Fort Knox, Kentucky – July 31, 2017, Princeton, New Jersey) was an American mathematician, specializing in group theory. O'Nan received his PhD in 1970 from Princeton University under Daniel Gorenstein with thesis A Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field. He was a professor at Rutgers University. In 1976 he found strong evidence for the existence of a sporadic group, which Charles Sims constructed. The group is commonly called the O'Nan group after O'Nan. The O'Nan–Scott theorem in group theory is also named after O'Nan, who discovered it independently from Leonard Scott. It describes the maximal subgroups of the symmetric groups.

Selected works Linear Algebra (= Eagle Mathematics Series. vol. 2A). Harcourt Brace Jovanovich, New York NY, 1971, ISBN 0-15-518558-6 (2nd edition.1976, ISBN 0-15-518560-8; 3rd edition. with Herbert Enderton. Harcourt Brace Jovanovich, San Diego CA, 1990, ISBN 0-15-551008-8). o'Nan, Michael E. (1975). "Normal structure of the one-point stabilizer of a doubly-transitive permutation group. I" (PDF). Bull. Amer. Math. Soc. 214: 1–42. doi:10.1090/s0002-9947-1975-0393207-3. MR 0393207. o'Nan, Michael E. (1975). "Normal structure of the one-point stabilizer of a doubly-transitive permutation group. II" (PDF). Bull. Amer. Math. Soc. 214: 43–74. doi:10.1090/s0002-9947-75-99942-0.

References

Worked examples

Example 1 — a first encounter with Michael O'Nan

Start with the simplest possible case. Write down what Michael O'Nan 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 Michael O'Nan 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 Michael O'Nan 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 Michael O'Nan

In research: Michael O'Nan 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 Michael O'Nan 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: Michael O'Nan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 2017 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael O'Nan 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.

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How to study Michael O'Nan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Michael O'Nan 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 Michael O'Nan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Michael O'Nan in simple terms?

Why does Michael O'Nan 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 Michael O'Nan?

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 Michael O'Nan.