Results 31 to 40 of about 116,475 (312)
Index graphs of finite permutation groups
Indonesian Journal of Combinatorics, 2022 Let G be a subgroup of Sn. For x ∈ G, the index of x in G is denoted by ind x is the minimal number of 2-cycles needed to express x as a product. In this paper, we define a new kind of graph on G, namely the index graph and denoted by Γind(G). Its vertex
Haval Mohammed Salih
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The Dade group of a metacyclic $p$-group. [PDF]
, 2003 The Dade group $D(P)$ of a finite $p$-group $P$, formed by equivalence classes of endo-permutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of $P$ and it is ...
Mazza, Nadia
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Sync-Maximal Permutation Groups Equal Primitive Permutation Groups [PDF]
, 2021 The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational problems related to synchronization and to the length of synchronizing words.
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Permutation Polytopes of Cyclic Groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices.
Barbara Baumeister +3 more
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Signed graphs and signed cycles of hyperoctahedral groups
Electronic Journal of Graph Theory and Applications, 2023 For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices.
Ryo Uchiumi
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On base sizes for symmetric groups [PDF]
, 2011 A base of a permutation group G on a set is a subset B of such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base.
Guralnick, Robert M. +7 more
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The Fixity of Permutation Groups
Journal of Algebra, 1995 By definition, the fixity of a finite permutation group \(G\) is the maximal number of fixed points of a non-identity element of \(G\); so if \(f\) denotes the fixity of \(G\) and \(n\) the degree of \(G\) then \(n-f\) is the minimal degree of \(G\). The authors prove some general theorems on transitive permutation groups \(G\) with given fixity \(f>0\)
Saxl, J., Shalev, A.
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On Eigenvalues of Permutation Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 Let λ1(G), λ2(G),..., λs(G) be the distinct eigenvalues of G with multiplicities t1, t2,..., ts, respectively. The multiset {λ1(G)t1, λ2(G)t2,..., λs(G)ts} of eigenvalues of A(G) is called the spectrum of G.
Sima Saadat-Akhtar, Shervin Sahebi
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The group of endotrivial modules in the normal case. [PDF]
, 2007 The group of endotrivial modules has recently been determined for a finite group having a normal Sylow $p$-subgroup. In this paper, we give and compare three different presentations of a torsion-free subgroup of maximal rank of the group of endotrivial ...
Mazza, Nadia
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On the Movement of a Permutation Group
Journal of Algebra, 1999 If \((G,\Omega)\) is a permutation group, then the movement \(\text{move}(G)\) is the supremum of \(\{|\Gamma^g\setminus\Gamma|:\Gamma\subseteq\Omega,\;g\in G\}\). If \(G\) has no fixed points, \(n:=|\Omega|\), and \(\text{move}(G)=m\) is finite, then \(n\leq 5m-2\), by a result of \textit{C. E. Praeger} [J. Algebra 144, No.
Neumann, P, Praeger, C
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