On this paper http://www.math.cornell.edu/~kbrown/6310/computation.pdf I read : This makes it easier for you to draw Schreier graphs as you read, which I encourage you to do. …

Given a transformation $t$ from the transformation semigroup $T_{n}$, if you take powers of $t$ under composition you get a length $s$ stem followed by a cycle. Permutations by def …

Definition / Question Definition: Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$. Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the …

Suppose that $\lambda_1,\lambda_2,\lambda_3$ are partititions of $n$. When do there exist permutations $\sigma_1,\sigma_2,\sigma_3 \in S_n$ such that (1) $\sigma_1\sigma_2\sigma_ …

Is there any routine technique to find a set of permutations which generate a Sylow 2-subgroup of the symmetric group $S_{2^{r−1}}$?

I am interested in automorphisms of graphs and in using tools from permutation groups (especially such as in Wielandt's text on finite permutation groups, which I have been studyin …

The symmetric group $S_n$ acts on $[n]:=\{1,\ldots,n\}$, thereby inducing an action on the set $$\wp_k(n)=\{\: A\subseteq[n] \::\: \#A=k \:\}$$ of subsets of cardinality $k$, simpl …

Let $\Gamma=Cay(G,S)$ be a Cayley graph over a group $G$, $H$ be a proper subgroup of $G$ and $\Sigma=Cay(H,T)$ where $S$ and $T$ are inversed-closed subsets of $G$ and $H$ not con …

Let $G$ be a finite permutation group acting transitively, but not regularly, on a set $V$. Let $H$ be the stabilizer of some point $v\in V$, and suppose that $H$ acts 2-transitive …

A permutation group $G \lt S_n$ is called generously transitive, if for each $i,j$ there exists a permutation that interchanges them. Is there a reasonable classification of such ( …

New formulation of the question: Let $n \in \mathbb{N}$. Is it true that for any $a, b, c \in \mathbb{N}$ satisfying $1 < a, b, c \leq n-2$ the symmetric group ${\rm S}_n$ has …

Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$. Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class transposition $\tau_{r_1(m_1), …

I just came back from a beach which features a large Rubik's cube (2m high). The base of the cube is not visible and the top is not coloured. The four vertical sides are each divi …

What is the maximal order $f(n)$ of a metacyclic (metacyclic group is the extension of a cyclic group by a cyclic group) transitive permutation group of degree $n$? It can be easil …

Let $G$ be a transitive group on $\Omega$. Every orbits of $G$ on its natural action on $\Omega\times\Omega$ is called an orbital of $G$ on $\Omega$. For each orbital $\Delta$ of $ …