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 Yearling
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Jan
29
awarded  Yearling
Oct
23
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
fixed title to reflect my question
Oct
22
accepted Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
Oct
22
comment Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
How does it look now?
Oct
22
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
made title more specific
Oct
21
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
final fix of the sum
Oct
21
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
tried fixing the sum
Oct
21
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
tried fixing the sum
Oct
21
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
tried making displaymath environment
Oct
21
revised Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
added 6 characters in body
Oct
21
asked Counting cyclic subgroups of order $p^{2}$: $p$ an odd prime vs. $p=2$
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
comment 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
comment In what sense is the classification of all finite groups “impossible”?
I had the arxiv link in mind.
Sep
10
comment 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
comment 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.