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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/…)
Jul
6
awarded  Revival
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
awarded  Constituent
Jun
8
awarded  Constituent
Jun
8
awarded  Caucus
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
5
revised On the group of signed permutations?
made proof independent of Taylor's book
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.
May
23
answered On the group of signed permutations?
May
21
comment Find the subgroups of index two of this finite semi-direct product
@user1729: No problem, it happened to me before, too (and probably to everybody else).