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seen Apr 9 at 18:27

Dec
24
comment Prime divisor in the Automorphism group
Take a look at the Suzuki groups, according to wikipedia they can have automorphisms of order $r = 3$.
Dec
24
comment Prime divisor in the Automorphism group
Do you want $G$ to be non-abelian?
Nov
25
comment Maximal soluble subgroups in a parabolic subgroup of finite classical simple group
If you ask the same question here and on mathoverflow, please give a link to the other page to avoid duplicated work by people not checking both pages!
Nov
15
comment Isomorphism between centralizer and semi direct product
Hint: Let $\sigma\in S_{mb}$ be your product of $m$ disjoint $b$-cycles. As a first step you should be able to show that elements centralizing $\sigma$ permute the orbits of $\langle\sigma\rangle$.
Nov
9
comment If a finite group has $\geq p+1$ Sylow $p$-subgroups (of order $p^n$), then there are $\geq p^{n+1}$ elements in the Sylow $p$-subgroups
@JackSchmidt: They are all in Sylows. If they are not in distinct Sylows, the intersection is not maximal.
Nov
9
comment If a finite group has $\geq p+1$ Sylow $p$-subgroups (of order $p^n$), then there are $\geq p^{n+1}$ elements in the Sylow $p$-subgroups
@DerekHolt: Yes, this was the idea.
Nov
9
comment If a finite group has $\geq p+1$ Sylow $p$-subgroups (of order $p^n$), then there are $\geq p^{n+1}$ elements in the Sylow $p$-subgroups
Hint: Take $Q$ be maximal among the intersections of $p$-Sylow subgroups. How many $p$-Sylow subgroups contain $Q$, and what do you know about their intersections? [Apply Sylow's theorem to $N_G(Q)$.]
Nov
7
comment Number of solutions of $x^d = 1_G$ .
See also mathoverflow.net/questions/109027/…
Nov
7
comment Prove that there are no simple groups of order 224.
There are even less $2$-Sylows ($G \to S_7$). [I guess you mean injective in the last sentence.]
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
31
answered A problem dealing with Sylow's subgroups
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/…)