A paper with this title has just gone on the arXiv, 2311.07995. The random graph, discussed at length here earlier, has the property of homogeneity: any isomorphism between finite subgraphs can be extended to an automorphism of the whole graph. Now unfortunately there are very few finite homogeneous graphs. They were all found by Tony…

Peter Cameron's Blog

20.11.2023

Coherent permutation groups | Peter Cameron's Blog

This post, in a sense, follows on from the previous one, though I won't explain the connection just yet. Here is another property of permutation groups which occurred to me last night. I have no idea yet whether it is worth anything at all, but I am open to ideas. Let G be a group…

Peter Cameron's Blog

27.11.2023

“Words that tear and strange rhymes” | Peter Cameron's Blog

In his youth, Paul Simon thought of himself as a poet: On a tour of one-night stands My suitcase and guitar in hand And every stop is neatly planned For a poet and a one-man band He thought about his craft: My thoughts are scattered and they're cloudy They have no borders, no boundaries They…

Peter Cameron's Blog

28.11.2023

Covers of groups | Peter Cameron's Blog

Here is the second of these discussions of elementary problems on finite groups with unexpected ramifications. This topic was suggested to me by Hamid Reza Dorbidi form Jiroft, Iran. Let F be a finite set of finite groups. A finite group G is a cover of F if every group in F is isomorphic to…

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EPPA numbers of graphs | Peter Cameron's Blog

Coherent permutation groups | Peter Cameron's Blog

“Words that tear and strange rhymes” | Peter Cameron's Blog

Covers of groups | Peter Cameron's Blog

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