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May
18 |
comment |
Groups that do not exist
It seems I remembered correctly. books.google.com/… |
Jan
29 |
awarded | Yearling |
Dec
9 |
comment |
Generalizations of the Four-Color theorem
$K_{7}$ in the torus has a nice algebraic description: Start with the graph formed by the Eisenstein integers, where $a$ is adjacent to $b$ means $|a-b| = 1$. Every vertex of this graph has degree 6, and it's planar. To make the plane a torus, we quotient by a lattice. To make this well-defined for how we identify vertices and edges, that lattice has to be an ideal. Choose an ideal of norm 7, like $(2+\sqrt{-3})$, and we now have 7 vertices (all have degree 6), yielding $K_{7}$. I don't know if replacing the Eisenstein ring with structures like the Hurwitz ring gives nice generalizations. |
Nov
18 |
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What makes the amenability of Thompsons group $F$ such a tricky problem?
The amenability of Thompson's group does not appear to be an isolated instance of this. The complexity of graph isomorphism is somewhat similar, and led the author of this paper to use the term "disease": onlinelibrary.wiley.com/doi/10.1002/jgt.3190010410/pdf So now write 'The Thompson Group Amenability Disease' or something like that? And maybe 'The Jacobian Conjecture Disease' while we're at it? What other examples of 'diseases' are out there? |
Nov
18 |
answered | Why do Bernoulli numbers arise everywhere? |
Sep
24 |
awarded | Autobiographer |
Sep
11 |
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In what sense is the classification of all finite groups “impossible”?
I had the arxiv link in mind. |
Sep
10 |
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In what sense is the classification of all finite groups “impossible”?
1. Can we make that expository paper about wild linear algebra problems community wiki? 2. Speaking of wildness and computational complexity, how do those problems behave when the field of interest is finite? Simultaneous conjugacy of ordered pairs of matrices is, for example, obviously in NP. |
Sep
6 |
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What are smallest finite images of triangle groups?
It is worth noting that there are finite simple groups whose simplicity cannot be proved this way. Since the $(2,3,5)$ triangle group is isomorphic to $A_{5}$, $A_{6}$ and $PSU_{4}(2)$ cannot be proven simple this way. I am not sure if there are any other examples. |
Jul
7 |
answered | Variations to Cayley's Embedding Theorem for Groups |
Jul
6 |
accepted | Subgroup property stronger than being characteristic |
Jul
3 |
revised |
Subgroup property stronger than being characteristic
"without having" --> "instead of having" because "< |
Jul
3 |
answered | Fantastic properties of Z/2Z |
Jul
3 |
comment |
Subgroup property stronger than being characteristic
Geoff, I am impressed by the nontrivial extent to which you read my mind -- I did not know the Thompson subgroup always did this, but I was trying to get a better handle on some local analysis. |
Jul
2 |
asked | Subgroup property stronger than being characteristic |
Jul
2 |
awarded | Curious |
Jun
20 |
awarded | Popular Question |
May
27 |
awarded | Enlightened |
May
27 |
awarded | Nice Answer |
May
1 |
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Non-trivial consequences of Baer's theorem and Lucchini's theorem in subnormality theory
A nice consequence I've encountered of the Baer-Suzuki theorem: |