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21h
comment Is every nonabelian finite simple group a quotient of a triangle group $(a,b,c)$ with $a,b,c$ coprime?
@NickGill : Yes, probably, thanks. I think the version I stated was already a corollary of Thompson's N-group paper, which dates to late 60s or early 70s, so Thompson has priority on that particular result, or it may be P.X. Gallagher. Of course, people have done much better since using CFSG, including the paper you mention.
1d
answered Is every nonabelian finite simple group a quotient of a triangle group $(a,b,c)$ with $a,b,c$ coprime?
2d
awarded  matrices
2d
comment What are the 2-generated subgroups of the special linear group $SL(2, q)$ over a finite field?
@DerekHolt :Thanks Derek, I wold have missed that. Presumably the outer automorphism of order $2$ is realised by an element of order 4?
2d
revised What are the 2-generated subgroups of the special linear group $SL(2, q)$ over a finite field?
incorporated Derek Holt's remark
2d
answered What are the 2-generated subgroups of the special linear group $SL(2, q)$ over a finite field?
Jul
19
revised A representation of a finite group where every nonzero vector has a trivial stabilizer
Added general remarks
Jul
19
comment Counting subspaces
In $V/U$ you are reduced to counting subspaces which have zero intersection with $W_{1} \cap W_{2}$ (by the way, I don't see the claim that $V/U$ is a direct sum as you state). There is still work to be done, but it's an easier situation.
Jul
19
comment Counting subspaces
I think the way to deal with the first question is to choose an $r^{\prime}$-dimensional subspace $U$ of $W_{1} \cap W_{2}$ and work in $V/U$. The number of choices for $U$ is easily calculated.
Jul
17
comment A representation of a finite group where every nonzero vector has a trivial stabilizer
@Derek Holt: I agree that there is not much to be learned from this question which is not covered by the earlier question and its answers.
Jul
17
revised A representation of a finite group where every nonzero vector has a trivial stabilizer
added extra information + typos
Jul
17
answered A representation of a finite group where every nonzero vector has a trivial stabilizer
Jul
14
awarded  Necromancer
Jul
14
revised Why can't a nonabelian group be 75% abelian?
mentioned non-finite case
Jul
13
awarded  Guru
Jul
10
comment Unsolvability of a Quintic and its link with “Simplicity” of $A_{5}$
As I said, my comments were "just out of interest", and I was not trying to make a comparison about relative importance of various viewpoints on Galois Theory (I was not the downvoter by the way).
Jul
10
comment Unsolvability of a Quintic and its link with “Simplicity” of $A_{5}$
Just out of interest: Many Galois theory texts prove simultanneously the simplicity of $A_{n}$ for $n >4$ first, but the fact that $A_{5}$ is simple is easy to prove directly (and the fact that $A_{5}$ is not solvable is even easier, since $A_{5}$ has no non-identity normal $p$-subgroup for any prime $p$, which is almost obvious). Once $A_{5}$ is known to be simple, a pretty easy induction gives $A_{n}$ simple for $n > 5.$
Jul
10
awarded  Good Answer
Jul
9
awarded  Enlightened
Jul
9
comment Why can't a nonabelian group be 75% abelian?
@j.p.: Notice that the two facts are interrelated. If we had $[G:Z(G)] < 4$, then every element $x \in G \backslash Z(G)$ would commute with at least $2|Z(G)|$ elements, so with more than $\frac{|G|}{2}$ elements, a contradiction.