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May
4
accepted Finding an ideal such that $\mathbb{Z}[x]/I \cong \mathbb{Z}[i]$.
May
4
comment Finding an ideal such that $\mathbb{Z}[x]/I \cong \mathbb{Z}[i]$.
If understand this correctly: $f$ is the evaluation homomorphism, if we restrict the domain of $f : \mathbb{Z}[x] \to \mathbb{Z}[i]$ the same still holds. However, the first isomorphism theorem implies that the quotient group is isomorphic to this subgroup. However, $f$ is also surjective, so the quotient group is isomorphic to $\mathbb{Z}[i]$?
May
4
asked Finding an ideal such that $\mathbb{Z}[x]/I \cong \mathbb{Z}[i]$.
May
1
comment Show that if $x ≡ 1 (\text{mod } λ)$, then $x^3 ≡ 1 (\text{mod } λ^3)$…
@Ebearr: Sorry my bad. (Referring to deleted answer) I guess it seemed a little too simple. Haha. Should of thought of that.
Mar
28
comment Proving that a sequence is increasing
Cleaner than what I had wrote. +1 :) Also, I had a small hole in my writing now that I think about it...
Mar
20
accepted Can I use Burnside's Theorem? Or should I take a different approach for this proof?
Mar
20
comment Can I use Burnside's Theorem? Or should I take a different approach for this proof?
Thank you for the response. Just to make sure I am understanding this: $3|[G : G_x]$ since $|G|= 3^3$ And we know that $|G|/|G_x|$ must be an integer, resulting in either $3^3$, $3^2$ or $3$, hence $|X'| \equiv 32 \mod 3$ meaning $|X'|$ has a strong lower bound of at least $2$ (since 32 mod 3 = 2)?
Mar
20
asked Can I use Burnside's Theorem? Or should I take a different approach for this proof?
Mar
19
accepted How do you apply an element on the left of a permutation?
Mar
19
comment How do you apply an element on the left of a permutation?
@ZachGershkoff: I was testing some small cases for a larger problem. I do not believe I am allowed to discuss the question that motivated this question, but I believe there was probably a flaw in the original question.
Mar
19
comment How do you apply an element on the left of a permutation?
Hmm, I was testing out small cases for a larger problem. After reviewing your answer and the comments, I believe the question that motivated this question has a flaw in it. I would post the original but, I do not believe I am allowed to do so. Thanks for the help!
Mar
19
asked How do you apply an element on the left of a permutation?
Mar
19
accepted What about my proof is “nonsense”?
Mar
18
answered What about my proof is “nonsense”?
Mar
18
comment What about my proof is “nonsense”?
@MikeMiller: I was thinking, that $x = ah$ for some $a \in G$ and $h \in H (\leq G)$, by closure of multiplication it has to be a member of $G$? Does this not make that much sense?
Mar
18
asked What about my proof is “nonsense”?
Mar
17
comment When does function composition commute?
I think the example is correct, but the math is wrong: $f(g(x)) = (x^2)^3 = g(f(x)) = (x^3)^2 = x^6$
Mar
16
comment Help with proving property of Rubik's cube.
@vadim123: Now that you say it, I can see it. There always exists a side that can be rotated four times for $C_2$. But you can do this to to get two other sides that don't touch $C_1$ and touch all 7 other cubicles. Thank you for the help!
Mar
16
asked Help with proving property of Rubik's cube.
Mar
14
accepted How should I continue my proof of this cycle property? (And did I make a mistake?)