Prometheus
Reputation
5,000
97/100 score
 Jan 26 comment If $M$ is normal and $M \cap U = U'$ for some special subgroup $U$, then $M / G'$ is a Hall-subgroup of $G / G'$. ok, that makes more sense Jan 26 comment If $M$ is normal and $M \cap U = U'$ for some special subgroup $U$, then $M / G'$ is a Hall-subgroup of $G / G'$. What are the conditions on $G'$? Is it just a normal subgroup of $G$ that is contained in $M$? If so, then it is enough to show for $G'=\{e\}$, but then you have no condition on $M$ other than it is normal in $G$. In any way, it seems that the group $G'$ is irrelevant for the proof. Jan 21 comment Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$ @J.G edited my answer Jan 21 revised Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$ full proof Jan 21 answered Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$ Jan 5 answered Maximal number of partial limits Jan 5 reviewed Approve Maximal number of partial limits Jan 4 comment Importance of diagonal (topology) @MikeMiller while I am a bit rusty on my algebraic geometry, I do remember that every affine scheme should be separated, which is the "right" analog for Hausdorffness in algebraic geometry. Jan 4 answered Are these two statements involving inf and sup equivalent? Jan 4 answered Importance of diagonal (topology) Jan 4 revised Embedding fields into the complex numbers $\mathbb{C}$. edited title Jan 3 comment The central product of two cyclic subgroups of prime power order for one $p$ is isomorphic to direct product of two cyclic groups of prime power order @Stefan I think that generators and relations is the easiest way to present this solution. The main idea here was to choose a new "basis" for the group and use the relations in order to figure out the right basis to choose. Jan 3 answered The central product of two cyclic subgroups of prime power order for one $p$ is isomorphic to direct product of two cyclic groups of prime power order Jan 3 answered Automorphism of cyclic $p$-group Jan 2 revised In $a^n \equiv b^n \pmod m$, does $n$ have to be an integer? added 109 characters in body Jan 2 comment In $a^n \equiv b^n \pmod m$, does $n$ have to be an integer? @ThomasAndrews You are correct. Though in this case, if $m$ is prime then it is well defined whenever you don't take the inverse of zero. Jan 2 answered In $a^n \equiv b^n \pmod m$, does $n$ have to be an integer? Jan 2 answered Is my solution correct? (primes of the form $a^2+b^2d$ and their principal ideals) Jan 1 comment Finding the limit of the sequence $(1 - 1/\sqrt 2) \dotsm ( 1 - 1/\sqrt {n+1})$ Your inequalities are in the wrong direction Dec 31 awarded Enlightened