# Tagged Questions

Cayley graphs are graphs obtained from a group $G$ in a such way that vertices are elements of the group and edges are added using some generating set $S\subseteq G$.

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### If a finite group G is a normal subgroup of the automorphism group of any connected Cayley graph thereof, is it realizable over Q?

The question is in the title: let $G$ be a finite group, and assume it is a normal subgroup of the automorphism group of any of its connected Cayley graphs. Does this imply that $G$ is the Galois ...
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### Hatcher Covering Spaces Ex. 11 & 31 and Surjectivity of the Covering Map

I am confused by the statements of a couple of the exercises in Section 1.3 of Hatcher. I think they need additional hypotheses that are not reflected in Hatcher's errata. Exercise 11: Construct ...
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### Cayley graph of the fundamental group of the 2-torus

Does anybody knows some description or some good picture on the internet for the Cayley graph of the fundamental group of the 2-torus, when this is constructed by connected sum of two torus. I know, ...
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### Plot Cayley graphs for generic element groups

I'm a beginner in Abstract Algebra, currently trying to solve all exercises in "A Book of Abstract Algebra" by Pinter. I was wondering if there is a way to draw Cayley graphs for generic element ...
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### Find all permutation sequences with only neighbor swaps

I am trying to essentially do what was done at this link, except for five elements instead of four. The link gives all of the possible sequences of permutations of four elements with the following 2 ...
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### Cayley graph with minimal generating set?

The answer to this question could be trivial ! Definition: Let $G$ be a group and $S$ a symmetric subset of $G$ (i.e., $s \in S$ iff $s^{ ā1} \in S$), the Cayley graph $Cay(G; S)$ of $G$ w.r.t. $S$ ...
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### How to construct a Cayley Table? [closed]

I have a set G = {e,a,b,c,d,f,g,h,i,j,k,l,m,n,o,p} which forms a group, (G, *) which is shown in the Cayley Digraph below. How do I go about constructing a Cayley table of (G,*), assuming e is the ...
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### Cayley graph for Frieze groups

I wonder how I can draw the Cayley graph for Frieze groups? For the group p11g with translations and glide reflections only (and a translation is obtained by two glide reflections), how do I show ...
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### on Cayley diagrams

is the picture the Cayley Graph of the group $\langle a,b,c\mid a^2, b^2,c^2\rangle$ ? What would it be for $\langle a,b,c\mid a^2b^2c^2\rangle$?
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### Proof: directed cycle?

A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in the same direction. In a directed graph, a set of edges which contains at least one edge (or arc) ...
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### Cayley graphs of finite 2-generator groups

Let $G=\left<a,b\right>$ be a finite 2-generator group and $\Gamma$ its Cayley graph with respect to $\{a,b\}$. Is it true that $\Gamma\setminus\{e,f\}$ is connected for two arbitrarily chosen ...
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### Are These Graphs Circulant?

We will say a circulant graph is a graph whose adjacency matrix is circulant (even if the graph is disconnected). Let $R$ be a Dedekind domain, and let $I$ be an ideal of $R$ such that $R/I$ is finite ...
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### s4ās2 visually?

What does the polytope whose symmetry is (exactly, not larger isomorphisms) s4ās2 look like? Does anyone know of a full decomposition of its construction, i.e. lattices, hasse diagrams, cayley graphs, ...
I need some help sorting out a construction of a group out of the vertices of a digraph with a certain property. I'll just throw some definitions here first... Definitions. An alphabet $A$...