Results 11 to 20 of about 13,348,296 (358)
Wave-Shaped Round Functions and Primitive Groups [PDF]
Advances in Mathematics of Communications, 2018 Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key ...
Aragona, Riccardo +4 more
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Countable Primitive Groups [PDF]
Geometric and Functional Analysis, 2007 39 pages, 2 figures. The first revision generalizes our previous paper "Infinite primitive groups" from the setting of finitely generated groups to countable groups.
Gelander, Tsachik, Glasner, Yair
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Imprimitive permutations in primitive groups [PDF]
Journal of Algebra, 2017 The goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a
J. Araújo +5 more
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Groups, Geometry, and Dynamics, 2007 A primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its orbits. We prove that finite extremely primitive groups are of affine type or almost simple. Moreover, we determine the affine type examples up to finitely many exceptions.
Mann, Avinoam +2 more
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Primitive Groups Synchronize Non-uniform Maps of Extreme Ranks [PDF]
J. Comb. Theory B, 2014 Let $\Omega$ be a set of cardinality $n$, $G$ a permutation group on $\Omega$, and $f:\Omega\to\Omega$ a map which is not a permutation. We say that $G$ synchronizes $f$ if the semigroup $\langle G,f\rangle$ contains a constant map.
Araújo, João, Cameron, Peter J.
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OVERGROUPS OF PRIMITIVE GROUPS [PDF]
Journal of the Australian Mathematical Society, 2009 Abstract We give a qualitative description of the set 𝒪 G (H) of overgroups in G of primitive subgroups H of finite alternating and symmetric groups G, and particularly of the maximal overgroups. We then show that certain weak restrictions on the lattice 𝒪 G (H) impose strong restrictions on H and its overgroup lattice.
M. Aschbacher
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On Abelian Quotients of Primitive Groups [PDF]
Proceedings of the American Mathematical Society, 1989 It is shown that if G G is a primitive permutation group on a set of size n n , then any abelian quotient of G G has order at most n n . This was motivated by a question in Galois theory. The field theoretic interpretation of the result is that if M /
Aschbacher, Michael +1 more
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Finite primitive groups of small rank: symmetric and sporadic groups [PDF]
Journal of Algebraic Combinatorics, 2019 Mikhail Muzychuk, Pablo Spiga
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On the Saxl graphs of primitive groups with soluble stabilisers [PDF]
Algebraic Combinatorics, 2021 Let G be a transitive permutation group on a finite set Ω and recall that a base for G is a subset of Ω with trivial pointwise stabiliser. The base size of G , denoted b ( G ), is the minimal size of a base. If b ( G ) = 2 then we can study the Saxl graph
Timothy C. Burness, Hong Huang
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Overgroups of primitive groups, II
Journal of Algebra, 2009 Assume that \(\Omega\) is a set of finite order \(n\), \(G\in\{\text{Sym}(\Omega),\text{Alt}(\Omega)\}\), and \(H\) is a subgroup of \(G\) acting primitively on \(\Omega\). In this paper it is continued the study of the set \(\mathcal O_G(H)\) of overgroups of \(H\) in \(G\) [for part I cf. J. Aust. Math. Soc. 87, No.
M. Aschbacher
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