mathematics

George Glauberman

George Glauberman 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 George Glauberman rather than just read about it. In short: George Isaac Glauberman (born 1941) is a mathematician at the University of Chicago who works on finite simple groups. He proved the ZJ theorem and the Z* theorem.

Key takeaways

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

Reference excerpt

George Isaac Glauberman (born 1941) is a mathematician at the University of Chicago who works on finite simple groups. He proved the ZJ theorem and the Z* theorem. Born in New York City on March 3, 1941, Glauberman did his undergraduate studies at the Polytechnic Institute of Brooklyn, graduating in 1961, and earned a master's degree from Harvard University in 1962. He obtained his PhD degree from the University of Wisconsin–Madison in 1965, under the supervision of Richard Bruck. He has had 22 PhD students, including Ahmed Chalabi and Peter Landrock. He has co-authored with J. L. Alperin, Simon P. Norton, Zvi Arad, and Justin Lynd. In 1970 he was an invited speaker at the International Congress of Mathematicians at Nice. In 2012 he became a fellow of the American Mathematical Society.

Selected publications Glauberman, George (1964), "On loops of odd order", Journal of Algebra, 1 (4): 374–396, doi:10.1016/0021-8693(64)90017-1, ISSN 0021-8693, MR 0175991 Glauberman, George (1966), "Central elements in core-free groups", Journal of Algebra, 4 (3): 403–420, doi:10.1016/0021-8693(66)90030-5, ISSN 0021-8693, MR 0202822, Zbl 0145.02802 Glauberman, George (1968), "A characteristic subgroup of a p-stable group", Canadian Journal of Mathematics, 20: 1101–1135, doi:10.4153/cjm-1968-107-2, ISSN 0008-414X, MR 0230807, S2CID 124178077, archived from the original on 2011-08-07, retrieved 2009-12-12 Glauberman, George (1968), "Correspondences of characters for relatively prime operator groups.", Canadian Journal of Mathematics, 20: 1465–1488, doi:10.4153/cjm-1968-148-x, ISSN 0008-414X, MR 0232866, S2CID 124632069, archived from the original on 2011-08-07, retrieved 2009-12-12 Glauberman, George (1968), "On loops of odd order. II", Journal of Algebra, 8 (4): 393–414, doi:10.1016/0021-8693(68)90050-1, ISSN 0021-8693, MR 0222198 Bender, Helmut; Glauberman, George (1994), Local analysis for the odd order theorem, London Mathematical Society Lecture Note Series, vol. 188, Cambridge University Press, ISBN 978-0-521-45716-3, MR 1311244

See also Glauberman normal p-complement theorem

References

External links Home page of George Glauberman

Worked examples

Example 1 — a first encounter with George Glauberman

Start with the simplest possible case. Write down what George Glauberman 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 George Glauberman 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 George Glauberman 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 George Glauberman

In research: George Glauberman 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 George Glauberman 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: George Glauberman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1941 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for George Glauberman 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 George Glauberman in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what George Glauberman means in your own words.
Compare your version with the excerpt and mark what you missed.
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Frequently asked questions

What is George Glauberman in simple terms?

George Isaac Glauberman (born 1941) is a mathematician at the University of Chicago who works on finite simple groups. He proved the ZJ theorem and the Z* theorem.

Why does George Glauberman 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 George Glauberman?

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 George Glauberman.