Category Archives: exposition

a post aimed to teach something

Asymptotic group theory, 5

Now the conference is over. On the last morning, Marty Isaacs posed an interesting problem. Let p be a prime, and n a positive integer. Is there an infinite group in which exactly n elements are not pth powers? This … Continue reading

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Asymptotic group theory, 4

Thursday was a national holiday in Hungary, St Stephen’s Day if you are religious or traditional, Constitution Day if you are a communist. “The shrewd communists let the parliament pass the new constitution on August 20, 1949,” in the words … Continue reading

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Asymptotic group theory, 3

A Ramanujan graph is a connected finite graph of valency k whose eigenvalues (apart from k and −k) all have modulus at most 2√(k−1). This interval is the spectrum of the infinite k-valent tree T (regarded as an operator on … Continue reading

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Asymptotic group theory, 2

Inna Capdeboscq started proceedings this morning with a talk about one small part of the second-generation (Gorenstein–Lyons–Solomon) proof of the Classification of Finite Simple Groups. What she described will be volume 8 of the complete proof, if I remember correctly. … Continue reading

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Asymptotic group theory, 1

The conference opened with a talk by Yoav Segev on his construction, with Eliahu Rips and Katrin Tent, of infinite non-split sharply 2-transitive groups. A permutation group is sharply 2-transitive if any pair of distinct elements of the domain can … Continue reading

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Alex through the looking glass

A few years ago now, I wrote about the launch of Alex’s Adventures in Numberland, a maths book for the general public by Alex Bellos. This year, I have read the follow-up, Alex through the Looking Glass, which I got … Continue reading

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History of the Random Graph

That wonderful object, the countable random graph, was first considered by Erdős and Rényi in their paper on “Asymmetric graphs” in 1963. After proving that a large random finite graph (edges chosen independently with probability 1/2) has (with high probability) … Continue reading

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