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Category Archives: doing mathematics
I’d like to see this solved
Here is a problem that I would really like to see solved. I have spent quite a bit of time on it myself, and have suggested it to a few other people, but it still resists all attacks, though it … Continue reading
Posted in doing mathematics, open problems
9 Comments
Graphs on groups, 13
There are many results about the universality, or otherwise, of various graphs defined on groups: answers to questions of the form “for which graphs Γ is there a group G such that Γ is isomorphic to an induced subgraph of … Continue reading
Graphs on groups, 12
One thing I have learned from the project is that the most interesting question about graphs defined on groups is this: given two types of graph defined on a group G, what is the class of groups for which the … Continue reading
Posted in doing mathematics, exposition
Tagged enhanced power graph, independence graph, power graph, rank, supersoluble group
1 Comment
Graphs on groups, 11
A brief interlude to describe another recent preprint, and as in the preceding post I will concentrate on one result in the paper. I don’t know why it happens, but in this project one of the most interesting graph parameters … Continue reading
Posted in doing mathematics, exposition
Tagged clique number, nilpotent group, solubility graph, souble group
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Graphs on groups, 10
The lesson of this post and the next in the series is that the most interesting questions (to me, anyway) are not about the girth of the deep commuting graph but instead about the classes of groups G defined by … Continue reading
Posted in doing mathematics, exposition
Tagged 2-Engel group, commuting graph, conjugacy, Dedekind group, enhanced power graph, power graph
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Graphs on groups, 9
We continue to make progress with the graphs on groups project, but this post attempts to step back and look at the whole thing. What use is all this? Once, after I talked at a departmental colloquium at the University … Continue reading
Posted in doing mathematics, exposition, open problems
Tagged graph theory, group theory, number theory, open problems
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Clive Sinclair
Yesterday I read the news that Clive Sinclair has died. This brought back memories of my first encounter with personal computers nearly 40 years ago. At the time I had a demanding job and three small children, and I was … Continue reading
Posted in doing mathematics, history, open problems
Tagged Neil Calkin, sum-free sets, ZX Spectrum
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Graphs on groups, 8
The dark clouds seem to have lifted a bit. Perhaps now, that the last rush of conferences for a while is over, life can return to something like normality … For me the most significant event was the last in … Continue reading
Posted in doing mathematics, events, open problems
Tagged graphs and groups, matching number, power graph
3 Comments
A new constant?
This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading
Posted in doing mathematics, open problems
Tagged clique number, Euler's function, power graph
8 Comments
Graphs on groups, 2
I wrote the long post about this to try to write it out of my system. No luck … I mentioned in that survey that every finite graph is embeddable as induced subgraph in the enhanced power graph, deep commuting … Continue reading
Posted in doing mathematics, mathematics
Tagged commuting graph, enhanced power graph
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