0
votes
1answer
182 views

Factor group of quaternion group

I have $Q_8=\{I,A,A^2,A^3,B,AB,A^2B,A^3B\}$ where $A=\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ and $B=\begin{pmatrix} 0 & i \\ i & 0 \end{pmatrix}$ Now I take a look at $Q_8/N$ ...
1
vote
0answers
27 views

Degrees of parabolic subgroups

Suppose a finite reflection group $G$ has the degrees $d_1,\ldots,d_n$. Let $G^*$ be a parabolic subgroup of $G$. What are the degrees of $G^*$. Since $|G^*|$ divides $|G|$ it is clear that the ...
0
votes
0answers
28 views

Building invariant $S_n$ structures from two invariant $Z_n$ structures

Take two mathematical structures with a $Z_n$ symmetry (cyclic symmetry). Which are the different ways, in "gluing" these structures, to obtain a mathematical structure with a $S_n$ symmetry ...
2
votes
2answers
157 views

equivariant hyperplane sections

Suppose you are given a smooth algebraic variety $X$ inside a projective space $\mathbb{P}$ and that there is a linear action of a finite cyclic group $G$ on $\mathbb{P}$ which restricts to an action ...
1
vote
1answer
245 views

Fencing the Group size,and its implication to Finiteness of Tate-Shafarevich Group

This question is an interesting one,not like my previous one. Can we judge the size of a Quotient Group by seeing the size of its constituents ? To add something ,Suppose consider a group ...