Results 11 to 20 of about 113,466 (234)
McKay graphs for alternating and classical groups [PDF]
Transactions of the American Mathematical Society, 2021 Let $G$ be a finite group, and $ $ a nontrivial character of $G$. The McKay graph $\mathcal{M}(G, )$ has the irreducible characters of $G$ as vertices, with an edge from $ _1$ to $ _2$ if $ _2$ is a constituent of $ _1$. We study the diameters of McKay graphs for finite simple groups $G$.
Martin W. Liebeck +2 more
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Divisibility Graph for Symmetric and Alternating Groups [PDF]
Communications in Algebra, 2015 Let $X$ be a non-empty set of positive integers and $X^*=X\setminus \{1\}$. The divisibility graph $D(X)$ has $X^*$ as the vertex set and there is an edge connecting $a$ and $b$ with $a, b\in X^*$ whenever $a$ divides $b$ or $b$ divides $a$. Let $X=cs~{G}$ be the set of conjugacy class sizes of a group $G$. In this case, we denote $D(cs~{G})$ by $D(G)$.
Abdolghafourian, Adeleh +1 more
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Automorphism group of the complete alternating group graph [PDF]
Applied Mathematics and Computation, 2017 9 pages, 1 ...
Huang, Xueyi, Huang, Qiongxiang
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2-Arc-transitive Cayley graphs on alternating groups
Journal of Algebra, 2022 An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the study of $2$-arc-transitive Cayley graphs on $\mathrm{A}_n$ for arbitrary valency.
Jiangmin Pan, Binzhou Xia, Fugang Yin
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ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH [PDF]
Forum of Mathematics, Sigma, 2017 Given a finite group $G$, the generating graph $\unicode[STIX]{x1D6E4}(G)$ of $G$ has as vertices the (nontrivial) elements of $G$ and two vertices are adjacent if and only if they are distinct and generate $G$ as group elements. In this paper we investigate properties about the degrees of the vertices of $\unicode[STIX]{x1D6E4}(G)$ when $G$ is an ...
LUCCHINI, ANDREA, MARION, CLAUDE
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GRAPH SMALL CANCELLATION THEORY APPLIED TO ALTERNATING LINK GROUPS [PDF]
Journal of Knot Theory and Its Ramifications, 2012 We show that the Wirtinger presentation of a prime alternating link group satisfies a generalized small cancellation condition. This new version of Weinbaum's solution to the word and conjugacy problems for these groups easily extends to finite sums of alternating links.
Cunéo, Rémi, Short, Hamish
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Conjugacy growth series of some infinitely generated groups
, 2016 It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function.
Bacher, Roland, De La Harpe, Pierre
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Graf Konjugasi dari Hasil Kali Langsung Grup Alternating A4 dan Grup Simetri S3
Jambura Journal of MathematicsThis study investigates the structure of conjugacy graphs formed from the conjugacy classes in the alternating group A4, the symmetric group S3, and their direct product A4 × S3.
Muhammad Fikri Muammar +2 more
doaj +1 more source
On Alternating and Symmetric Groups Which Are Quasi OD-Characterizable
, 2017 Let $\Gamma(G)$ be the prime graph associated with a finite group $G$ and $D(G)$ be the degree pattern of $G$. A finite group $G$ is said to be $k$-fold OD-characterizable if there exist exactly $k$ non-isomorphic groups $H$ such that $|H|=|G|$ and $D(H)=
Moghaddamfar, Ali Reza
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A survey on the Turaev genus of knots
, 2014 The Turaev genus of a knot is a topological measure of how far a given knot is from being alternating. Recent work by several authors has focused attention on this interesting invariant. We discuss how the Turaev genus is related to other knot invariants,
Champanerkar, Abhijit, Kofman, Ilya
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