Tagged Questions

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When does the adjacency or incidence matrix of a graph have consecutive ones property?

Given a graph, what are some sufficient (and necessary) conditions to tell if its adjacency matrix has the consecutive ones property? Similar question for its incidence matrix? Note that a ...
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Group does not contain any elements of order $p^2$?

I am trying to show that the group of $3 \times 3$ upper triangular matrices over the field $\mathbb{F}_p$ with diagonal entries 1 does not contain any elements of order $p^2$ when $p \geq 3$. ...
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Algorithm to find conjugacy classes of subgroups/elements (in matrix groups)?

I'm looking for a simple (=doable to implement by myself) algorithm to compute the conjugacy classes of elements and subgroups of a given subgroup of $\text{P}{\Gamma}\text{L}(n,q)$. So given a group ...
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program to find matrix group given generators (Matlab)?

Given a small number of generators for a group of small (e.g. $3\times3$) matrices over a finite field $\mathbb{F}_p$ where $p$ is prime, how can we find all the elements of the group? The best I've ...
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Computing $\mathbb{C}[x,y]^G$ or $\mathbb{C}[x,y,z]^G$ where $G$ is a finite subgroup of $GL_n(\mathbb{C})$

My question is related to this link: Ring of Invariant $\mathbf{Question \;1}$. Let $$A = \left( \begin{array}{cc} 0 & -1 \\ 1& 0 \\ \end{array} \right).$$ Then $C= \langle A\rangle$ ...
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Elementary matrix operations on group

Given a matrix whose every element is an element of group Sn (Symmetric group of n objects). I want to apply Gaussian Elimination to convert it into row echelon form. I need to find out linearly ...
Is there a “natural” transitive action of $SL_2(\mathbb{F}_5)$ on a set with 5 elements?
I'm really looking for a "cute" way of showing that $SL_2(\mathbb{F}_5)$ is a double cover of $A_5$. The sort of action I am looking for is something like the action of $GL_2(\mathbb{F}_3)$ on ...
Let $\mathbb{F}_3$ be the field with three elements. Let $n\geq 1$. How many elements do the following groups have? $\text{GL}_n(\mathbb{F}_3)$ $\text{SL}_n(\mathbb{F}_3)$ Here GL is the general ...