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seen Sep 24 at 10:54

Oct
31
comment Theorems with an extraordinary exception or a small number of sporadic exceptions
No free group is abelian, with the exception of $\mathbb Z$.
Oct
31
comment A problem dealing with Sylow's subgroups
@Galoisfan: You can even streamline my proof a little by unifying the argument that every element normalizes some Sylow subgroup.
Oct
16
comment Is finite group theory still a fruitful area of research?
If you are interested, how a much improved proof of the classification of finite simple groups could look like, take a look at math.msu.edu/~meier/Preprints/CGP/cgp_abstract.html [This is a still active area, but technically quite difficult.]
Aug
30
comment A polynomial whose Galois group is $D_8$
Small typo: $F$-automorphism should be $\mathbb{Q}$-automorphism. As Dharam didn't specify the field (so I assume he doesn't care about it), I wonder why the solution on mathoverflow gets so many upvotes, but this generic solution didn't get any. Maybe you could mention what the fixed field for $G = S_n$ is, so that people recognize this solution from their algebra class...
Aug
23
comment Reference: Finite Groups and Geometry
The Geometry of the Classical Groups by D.E. Taylor.
Aug
16
comment Abelian subgroup of a group of order $2002$
@Serkan: With full details your approach should be shorter (and easier) than the one given by DonAntonio.
Aug
10
comment Uniqueness of conjugates of a subgroup.
You could also reread Geoff's answer to the question you linked to...
Aug
10
comment Uniqueness of conjugates of a subgroup.
You are trying to prove that $A$ is weakly closed in $B$. Look up this term (or "weak closure") in any group theory book. Often the case $B$ a $p$-Sylow subgroup is of interest.
Jul
30
comment Converting a (signed) permutation to a reduced word
From (9.22) in the book rsp. Claim (a) and (b) in my answer you can easily deduce that $\mathop{des}(\sigma)$ is essentially the same as $\mathop{D}(\sigma)\cap R$ (with $R$ the set of Coxeter generators): just identify $0$ with $(1\; -1)$ and $i>0$ with $(i\; i+1)$.
Jul
29
comment Converting a (signed) permutation to a reduced word
Another good source is chapter 9 of the book The Geometry of the Classical Groups by D.E. Taylor (combined with my answer to math.stackexchange.com/questions/106462/…)
Jun
22
comment Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
This question is related: math.stackexchange.com/questions/151931/…
Jun
8
comment A representation is semisimple if its restriction to a subgroup of index prime to Char(F) is semisimple
(12.8) in Aschbacher's book "Finite Group Theory" (directly before Maschke's theorem) proves the statement for $H$ a $p$-Sylow (considering also (12.6)). If someone feels like, please expand it into an answer...
Jun
7
comment On automorphism of some finite 2-group of class nilpotency two
@user1729: I'd call Derek a pro.
Jun
6
comment Set of zeroes of the derivative of a pathological function
@EwanDelanoy: According to mathworld.wolfram.com/MinkowskisQuestionMarkFunction.html the Minkowski question mark function is purely singular, which means its derivative is almost everywhere 0 (according to planetmath.org/encyclopedia/SingularFunction2.html). So it doesn't answer the 1st question.
Jun
2
comment Set of zeroes of the derivative of a pathological function
Take a look at the mean value theorem in J. Dieudonne's "Foundation of Modern Analysis" (8.5.1 in my edition) or at www.ms.unimelb.edu.au/~jjk/doc/MVT.pdf (Theorem 1b). Such a function does not exist...
May
31
comment (Regular) wreath product of nilpotent groups
@SteveD: You should mention your implicit assumption $p\ne q$ ;-). To user31899: To be even more concrete than Steve, take $A$ and $B$ as simple as possible, but violating the condition after "if and only if", e.g., take something like $A=C_3$, $B=C_2$.
May
30
comment If $a_n$ goes to zero, can we find signs $s_n$ such that $\sum s_n a_n$ converges?
@EwanDelanoy: For the greedy construction you get in the proof of your lemma the limit $M\cdot\sqrt{r}$ (if $b_{i+1}$ is perpendicular to the result you got for being greedy on $b_1, \dots, b_i$, and all $b_i$ having the same length).
May
30
comment A representation is semisimple if its restriction to a subgroup of index prime to Char(F) is semisimple
If I remember correctly, you can use the usual averaging argument for proving Maschke's theorem (just take the average over coset representatives of $H$ instead of over all elements of $G$)
May
25
comment Maximal subgroups of a finite p-group
You need the condition $G/U$ not cyclic.
May
24
comment What could the meaning of “invariant of $G$” be?
The lengths of the orbits of a point stabilizer are invariants of the permutation group $G$. So yes, it's an invariant of the group action. Different action have (generally) different subdegrees.