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Jun
30
accepted How to compute the automorphism group of split metacyclic groups?
Jun
25
comment How to compute the automorphism group of split metacyclic groups?
It is a brilliant idea to apply the Frattini Argument to $Q$. But I am just not sure how you get $\text{C}_A(G)=1$. I think you are using the fact that $G$ is embedded in $A$, and so any element cannot centralize $G$ or it will induce a trivial automorphism. But saying $G$ as the inner automorphism group, then the elements in $\text{C}_A(G)$ is just the elements that commutes with the inner automorphisms. In this sense can we still say $\text{C}_A(G)=1$? I am not sure.
Jun
23
comment How to compute the automorphism group of split metacyclic groups?
@j.p.:$\text{Aut}(\mathbb Z_p)=\mathbb Z_{p-1}$. So the kernel shouldn't be trivial. However, if we can show the kernel is $\mathbb Z_p$ then we are done.
Jun
23
comment How to compute the automorphism group of split metacyclic groups?
@anon: $k$ can be any integer that divides $p-1$. But I believe it doesn't affect the result.
Jun
23
asked How to compute the automorphism group of split metacyclic groups?
Feb
4
revised New proof about normal matrix is diagonalizable.
added 4 characters in body
Feb
4
answered New proof about normal matrix is diagonalizable.
Jan
29
awarded  Yearling
Sep
30
awarded  Explainer
Jul
2
awarded  Curious
May
24
revised Does every function with $f_x,f_y>0,f_{xx},f_{yy}<0$ with particular condition have to satisfy $f_{xy}/f_{xx} = -x/y$?
deleted 3 characters in body
May
24
comment Does every function with $f_x,f_y>0,f_{xx},f_{yy}<0$ with particular condition have to satisfy $f_{xy}/f_{xx} = -x/y$?
When you say $\infty$, it is $+\infty$ or $-\infty$?
May
21
answered Inverse of a sum of positive definite matrices
May
20
answered Proving $A+2B+3C+4D < 2.5$ with given conditions
May
20
comment If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
You may want to consider the fundamental theorem of Lebesgue integral calculus, which requires $f'(x)=0$ almost everywhere to get to your result. However, $\mathbb{Q}$ is far away from almost everywhere..
Feb
12
awarded  Nice Answer
Jan
29
awarded  Yearling
Sep
12
accepted Maximal abelian subgroups in a $p$-group are always normal?
Sep
12
comment Maximal abelian subgroups in a $p$-group are always normal?
thanks, I didn't realise it was so simple.
Sep
11
comment Maximal abelian subgroups in a $p$-group are always normal?
@DonAntonio, yeah, I am assuming the $p$-group is finite. But I am talking about maximal among abelian subgroups, not just maximal among any subgroups.