420 reputation
612
bio website
location
age
visits member for 3 years, 8 months
seen Apr 9 at 18:27

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?
Apr
14
comment Conjugacy Classes of subgroups in GL(n,p)
Take a look at the possible subspaces of $\mathbb{F}_p^n$ fixed by an element of order $p$ in $\mathrm{GL}(n, p)$. Do they all have the same dimension?
Mar
20
comment Non-Standard Deviation
Yes, there is something better. Yuval's suggestion wasn't just about avoiding the absolute value.
Feb
16
comment Permutation group proofs
For (2), as all elements of $S_n$ have finite order, $H_n$ is a subgroup of $S_n$ if and only if it is (non-empty and) closed under multiplication. Did you already try multiplying some elements of odd order to see if their product has odd order again? Just play around multiplying various $3$-cycles of $S_5$ as a start.
Jan
26
comment Showing $H$ is a normal subgroup of $G$
Does $H$ contain a unique $A$?
Jan
26
comment Showing $H$ is a normal subgroup of $G$
Should the map satisfy $\varphi(0) = A$? Maybe another equality helps you more...
Jan
26
comment Showing $H$ is a normal subgroup of $G$
Given a continuous map $\varphi:[0,1] \to G$, what do you know about the map $\varphi^A : x \mapsto A\cdot x\cdot A^{-1}$?
Jan
26
comment Showing $H$ is a normal subgroup of $G$
Given $A_i \in H$ and $\varphi_i$ like in the definition of $H$ for $i=1, 2$, what do you know about $\varphi = \varphi_1 \cdot \varphi_2$ where $"\cdot"$ denotes pointwise multiplication of matrices?
Jan
3
comment Dividing in $\mathbb{Z}_m[x]/p(x)$
As you're calculating modulo $3$, you have $2 = -1$.
Dec
30
comment Simplicity of $A_n$
Could you maybe elaborate more how you would prove the simplicity of $A_n$ using your ideas? I don't see how to do it, but would be very interested in it.
Dec
23
awarded  Enthusiast
Dec
20
comment A finite length module is the direct sum of the image and kernel of a projection-like endomorphism
@Green Iden: You are welcome. After the deadline for your homework assignment, you could post your solution as answer.
Dec
19
comment A finite length module is the direct sum of the image and kernel of a projection-like endomorphism
@Pete: Yes, the proof is quite similar.
Dec
19
comment A finite length module is the direct sum of the image and kernel of a projection-like endomorphism
@Green Iden: Yes.
Dec
19
comment A finite length module is the direct sum of the image and kernel of a projection-like endomorphism
@Pete: $f$ does not fulfill the condition $f\circ f = f$, but only $f\circ f(A) = f(A)$.
Dec
19
comment A finite length module is the direct sum of the image and kernel of a projection-like endomorphism
Did you already look at the subgroups $\mathrm{Ker}(f^n)$?