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May
10
asked Need help determining what this center is isomorphic to
May
8
accepted Help show the following isomorphism cannot exist.
May
8
comment Help show the following isomorphism cannot exist.
Ok, so I think I get it, I made a small typo in my question, but was able to follow through and get $v^2 - v + 1 = 0$. But still, $x^2 - x + 1 \not\in \langle g(x) \rangle$. Thanks!
May
8
revised Help show the following isomorphism cannot exist.
edited body
May
8
comment Help show the following isomorphism cannot exist.
I still applied simplifications as if it was $\mathbb{Z}_3$ if that is what you are wondering...
May
8
revised Help show the following isomorphism cannot exist.
added 4 characters in body
May
8
comment Help show the following isomorphism cannot exist.
Oops, sorry about that.
May
8
asked Help show the following isomorphism cannot exist.
May
5
comment a question about abstract algebra,the order of $\Bbb Z_{5}[x]/ (x^3+x+1)$
Beat me too it too. +1
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!