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Aug
9
comment Group of order $3^a\cdot5\cdot11$ has a normal Sylow 3-group
@Steve: Instead of counting you could repeat the first part of your proof with $N$ and $11$.
Aug
5
awarded  Yearling
Aug
4
comment If $|H|$ and $[G:K]$ are relatively prime, then $H \leq K$
@Geoff: You could also add a hint and a spoiler warning at the beginning of your (nice) answer and undelete it.
Aug
4
comment If $|H|$ and $[G:K]$ are relatively prime, then $H \leq K$
dls wrote "A hint would be perfect.". This is slightly more than a hint...
Aug
4
comment If $|H|$ and $[G:K]$ are relatively prime, then $H \leq K$
For a proof without using Sylow's theorem: take the order information from the isomorphism $KH/H \cong K/(K\cap H)$.
Jul
28
comment Does this class of cipher have a name? What weaknesses does it have?
I wouldn't feel comfortable encrypting two plaintexts with the same $g$.
Jul
25
comment Teach me a simple, efficient division algorithm
Take the long division algorithm as given in Knuth: The Art of Computer Programming, Vol. 2. In the 3rd edition this is Algorithm D in section 4.3.1 on page 272. Googling for the terms knuth "algorithm d" site:books.google.com I got as top link "Hacker's delight" where a C-version of that algorithm is given.
Jul
15
comment G a finite group, M a maximal subgroup; M abelian implies G solvable?
@7115763: You have to apply Burnside's normal $p$-complement theorem to each $p$-Sylow of $M$ (which are also $p$-Sylows of $G$ as $M$ is a Hall subgroup).
Jun
15
comment
@Isaac: Wouldn't be the upvotes-to-given-answers ratio a better measure than the upvotes-to-rep ratio? The latter punishes people giving few but brilliant answers. Is the upvotes-to-given-answers ratio somewhere available?
Jun
10
comment Abelian subgroups of p-groups
@Rahul: Did you read the second paragraph of Derek Holt's answer?
Jun
9
comment Abelian subgroups of p-groups
You have to read "Burnside's classic theorem" differently: Given a $p$-group of order $p^n$ there exists a normal abelian subgroup of order $p^m$ with $n\le m(m-1)/2$. You wrongly read it as "Given a $p$-group of order $p^n$ there exists for all $m$ with $n\le m(m-1)/2$ a normal abelian subgroup of order $p^m$.", which is clearly absurd as you could choose $m>n$.
Jun
4
comment is every subgroup of a semi-direct product of groups a semi-direct product of subgroups?
For case i) do you really want $G = \mathrm{GL}(n, K)$ or did you intend to write $Q = \mathrm{GL}(n, K)$?
May
23
comment The cycle structure of the permutation $a \mapsto ma \bmod{n}$
Did you try to solve your problem in the case $n$ is a prime? Then look at the case $n$ a prime power, and finally apply the Chinese Remainder Theorem.
May
13
revised Are there any generic thinking approaches for providing mathematical proofs to a given theorem
added hint about how to read proofs
May
13
awarded  Editor
May
13
revised Are there any generic thinking approaches for providing mathematical proofs to a given theorem
added three items
May
6
comment RSA: Creating a key of desired length
Choose the highest two bits of both numbers to be 11.
Apr
14
comment Conjugacy Classes of subgroups in GL(n,p)
@Alex: I'm very curious about this. How does the order help considering that there is also a cyclic group of the same order?
Apr
14
comment A proof of Sylow theorem
Sylow 3 (taking the numbering of the wikipedia) is a corollary of Sylow 1+2 by taking the action of the $G$ by conjugation on the set of $p$-Sylow subgroups.
Apr
14
comment Conjugacy Classes of subgroups in GL(n,p)
@Alex: Should (s)he compute the order of $\mathrm{GL}(n, p)$ just to get to know the group, or does the order of the group help in any way for the question?