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7h
comment When does normal maximal subgroup have prime index?
@NickyHekster he says $N$ is a maximal subgroup and is also normal, so t suffices to find a subgroup between $G$ and $N$ to contradict the maximality.
21h
comment When does normal maximal subgroup have prime index?
exactly, I hope this helped.
21h
comment Find the greatest common divisor of pairs of polynomials
use the euclidean algorithm.
21h
comment Wolfram|Alpha refuses to find the inverse of a large 6x6 matrix.
" I have no idea why the technology I so desperately rely on is failing me now." relying on wolframalpha is for noobs.
21h
comment When does normal maximal subgroup have prime index?
have you tried using the correspondence theorem ? (sometimes called 4th iso theorem).
1d
comment Prove that even $n$ can be partitioned to $\frac n2$ edges
There is no $\frac{n}{2}$ becuase I swapped $n$ with $2n$.
1d
comment Show that a ring $R$ is a division ring if and only if, for each nonzero $a\in R$, there is a unique element $b\in R$ such that $aba = a$.
your solution has some flaws, like for example, why does such an $r$ exist?
1d
comment Show that a ring $R$ is a division ring if and only if, for each nonzero $a\in R$, there is a unique element $b\in R$ such that $aba = a$.
this was totally in my homework last year, let me see if I an remember
1d
comment Prove that even $n$ can be partitioned to $\frac n2$ edges
What part is causing you trouble?
1d
comment Let $G$ be a group of order $35$. Prove that $G \cong C_5 \times C_7$.
if a subgroup is the only subgroup of its order then it is normal (because $gHg^{-1}$) is a subgroup with the same order as $H$)
1d
comment How do I memorize mathematical proofs?
Regarding the title: don't.
1d
comment Graph Theory Proof of Website Clicks
the website you are looking for is the website with the most links, this website can reach every other website with at most two clicks
1d
comment Graph Theory Proof of Website Clicks
I'll write it again, maybe it will be clearer now
2d
comment If $G$ and $G'$ are two finite group of same cardinal, then $G\cong G'$.
I think we also need $pq$ where $p<q$ and $q$ is not congruent to $1\bmod p$.
2d
comment If $G$ and $G'$ are two finite group of same cardinal, then $G\cong G'$.
Oh, you seem to be right.
2d
comment If $G$ and $G'$ are two finite group of same cardinal, then $G\cong G'$.
I am pretty sure there are at least two non-isomorphic groups of any cardinality except for $0,1$ and $p$ (where $p$ is prime).
2d
comment How do I prove that if $2\nmid n$ then $2|(n+1)$?
what can you use?
Feb
9
comment What is the probability that a psychic correctly “predicts” the outcome of at least 5 out of 10 coin flips?
yes${}{}{}{}{}$
Feb
9
comment How I can prove that for any natural number $n$ such that $30<n$, $\pi(4n-3)<n$?
it is true, we have $\pi(x)<1.3\frac{x}{\log x}$ for $x\leq 17$
Feb
8
comment Show that $1^k+2^k+\cdots+n^k$ is $\Omega (n^{k+1})$
because $1^k+2^k+3^k+\dots+n^k=\int\limits_0^n\lceil x \rceil ^kdx\leq\int\limits_0^n x ^kdx$